In this video we are going to understand about the Central LIMIT theorem.Support me in Patreon: https://www.patreon.com/join/2340909?Buy the Best book of Mac...Chebyshev’s Theorem Multiple Choice. applies to all samples. applies only to samples from a normal population. gives a narrower range of predictions than the Empirical Rule. is based on Sturges’ Rule for data classification. There’s just one step to solve this.This statistics video provides a basic introduction into Chebyshev's theorem which states that the minimum percentage of distribution values that lie within ... Note: Technically, Chebyshev’s Inequality is defined by a different formula than Chebyshev’s Theorem. That said, it’s become common usage to confuse the two terms ; A quick Google search for “Chebyshev’s Inequality” will bring up a dozen sites using the formula (1 – (1 / k 2 )). Chebyshev’s inequality says that in this situation we know that at least 75% of the data is two standard deviations from the mean. As we can see in this case, it could be much more than this 75%. The value of the inequality is that it gives us a “worse case” scenario in which the only things we know about our sample data (or probability …Proof. The theorem is trivially true if f is itself a polynomial of degree ≤ n. We assume not, and so dn > 0. Step 1. Suppose that f, pn has an alternating set of length n + 2. By Theorem 4, we have || f − pn || ≤ dn. As dn ≤ || f − pn || by the definition of dn, it follows that pn is a polynomial of best approximation to f.Sep 11, 2014 ... The situation for explicit integration in \eta is complementary to that in t. ... We also show that our method may be used to study more realistic ...Proof of the Theorem. To prove Chebyshev's Theorem, we start by using Chebyshev's inequality, which states that for any non-negative random variable X and any positive number k, the following inequality holds: P(X ≥ k) ≤ E(X)/k Where E(X) is the expected value of X. In this video, we look at an example of using Chebyshev's theorem to find the proportion of data contained within an interval that is of the form, the mean p...Chebyshev’s Theorem is a fact that applies to all possible data sets. It describes the minimum proportion of the measurements that lie must within one, two, or …Question: d. Using Chebyshev's Theorem, determine the range of prices that includes at least 94% of the homes around the mean. 3.27 The following data represent the number of touchdown passes per season thrown by the Benedict Arnold of the National Football League, Brett Favre (can you tell I'm 112 CHAPTER 3 | Calculating Descriptive Statistics …切比雪夫定理的这一推论，使我们关于算术平均值的法则有了理论根据．设测量某一物理量a，在条件不变的情况下重复测量n次，得到的结果X 1 ，X 2 ，…，X n 是不完全相同的，这些测量结果可看作是n个独立随机变量X 1 ，X 2 ，…，X n 的试验数值，并且有同一数学期望a。 。于是，按大数定理j可知 ...Jan 23, 2023 ... Pushing 1/4 of the data 2 standard deviations away from the mean (or pushing 1/9 of the data 3 standard deviations away, or 1/16 of it 4 ...Exercises - Chebyshev's Theorem. What amount of data does Chebyshev's Theorem guarantee is within three standard deviations from the mean? k = 3 in the formula and k 2 = 9, so 1 − 1 / 9 = 8 / 9. Thus 8 / 9 of the data is guaranteed to be within three standard deviations of the mean. Given the following grades on a test: 86, 92, 100, 93, 89 ...Chebyshev’s Theorem states that for any number k greater than 1, at least 1 – 1/k 2 of the data values in any shaped distribution lie within k standard deviations of the mean. For example, for any shaped …切比雪夫定理（Chebyshev's theorem）：适用于任何数据集，而不论数据的分布情况如何。 与平均数的距离在z个标准差之内的数值所占的比例至少为(1-1/z 2)，其中z是大于1的任意实数。. 至少75%的数据值与平均数的距离在z=2个标准差之内；Free Chebyshevs Theorem Calculator - Using Chebyshevs Theorem, this calculates the following: Probability that random variable X is within k standard deviations of the mean. How many k standard deviations within the mean given …Chebyshev's Theorem: Let X X be a discrete random variable with finite mean μx μ x and standard deviation σx σ x. Let k k be greater than 1 1. Then the probability that X X is more than k k standard deviations from the mean, μX μ …1. Chebyshev's inequality says that. P(|X − μ| > kσ) ≤ 1 k2 P ( | X − μ | > k σ) ≤ 1 k 2. where μ μ is the mean of X X and σ σ is its standard deviation. This is the probability of the random variable being more than k k standard deviations from the mean, and note that its maximum value goes down as k k gets large, as you would ...The above proof of a special case of Bernoulli’s theorem follows the arguments of P. L. Chebyshev that he used to prove his inequality and does not require concepts such as independence, mathematical expectation, and variance. The proved law of large numbers is a special case of Chebyshev’s theorem, which was proved in 1867 (in …Chebyshev’s inequality theorem provides a lower bound for a proportion of data inside an interval that is symmetric about the mean whereas the Empirical theorem provides the approximate amount of data within a given interval. This is my attempt to put the difference between the two theorems. Let me know if you have difficulties in ...Instructions: This Chebyshev's Rule calculator will show you how to use Chebyshev's Inequality to estimate probabilities of an arbitrary distribution. You can estimate the probability that a random variable X X is within k k standard deviations of the mean, by typing the value of k k in the form below; OR specify the population mean \mu μ ... This video shows you How to Pronounce Chebyshev (Russian mathematician) pronunciation.Learn how to say PROBLEMATIC WORDS better: https://www.youtube.com/watc...To apply Chebyshev’s theorem, you need to choose a value for k, an integer greater than or equal to 1. This value represents the number of standard deviations away from the mean you want to analyze. 6. Applying Chebyshev’s theorem. Now that you have the mean, standard deviation, and k value, you can apply Chebyshev’s theorem to calculate ...19.2 Chebyshev’s Theorem We’ve seen that Markov’s Theorem can give a better bound when applied to Rb rather than R. More generally, a good trick for getting stronger bounds on a ran-dom variable R out of Markov’s Theorem is to apply the theorem to some cleverly chosen function of R. Choosing functions that are powers of the absolute ...In this video I cover at little bit of what Chebyshev's theorem says, and how to use it. Remember that Chebyshev's theorem can be used with any distribution...This statistics video provides a basic introduction into Chebyshev's theorem which states that the minimum percentage of distribution values that lie within ...This lecture will explain Chebyshev's inequality with several solved examples. A simple way to solve the problem is explained.Other videos @DrHarishGarg Cheb...The mean price of RV's is $20,000 with a standard standard deviation of $400. Using Chebyshev's Theorem, find the minimum percent of homes within 1.3 standard deviations of the mean. Choose the ...Jan 20, 2019 · So Chebyshev’s inequality says that at least 89% of the data values of any distribution must be within three standard deviations of the mean. For K = 4 we have 1 – 1/K 2 = 1 - 1/16 = 15/16 = 93.75%. So Chebyshev’s inequality says that at least 93.75% of the data values of any distribution must be within two standard deviations of the mean. Feb 14, 2020 · By now (1987) Chebyshev's theorems have been superceded by better results. E.g., $$\pi(x)=\operatorname{li}(x)+O(x\exp(-c\sqrt{\log x}))$$ (see for even better results); further $\pi(x)-\operatorname{li}(x)$ changes sign infinitely often. More results, as well as references, can be found in , Chapt. 12, Notes. References Chebyshev’s inequality, in probability theory, a theorem that characterizes the dispersion of data away from its mean (average). The general theorem is attributed to the 19th-century Russian mathematician Pafnuty Chebyshev , though credit for it should be shared with the French mathematician Irénée-Jules Bienaymé, whose (less general) 1853 proof predated …this theorem in 1875 and Chebychev in 1878, both using completely different approaches [1]. Figure 1: Three different four-bar linkages tracing an identical coupler curve.Chebyshev’s theorem, also known as Chebyshev’s Inequality, states that the proportion of values of a dataset for K standard deviation is calculated using the equation:. Here, K is any positive integer greater than one. For example, if K is 1.5, at least 56% of the data values lie within 1.5 standard deviations from the mean for a dataset. If K is 2, at least 75% of the …Free Chebyshevs Theorem Calculator - Using Chebyshevs Theorem, this calculates the following: Probability that random variable X is within k standard deviations of the mean. How many k standard deviations within the mean given …Nov 21, 2023 · Chebyshev's inequality, also known as Chebyshev's theorem, is a statistical tool that measures dispersion in a data population that states that no more than 1 / k 2 of the distribution's values ... May 15, 2011 · This is a brief video concerning the premises of Chebyshev's Theorem, and how it is used in practical applications. Using Chebyshev's Theorem, what is the minimum percentage of recent graduates who have salaries between $22,400 and $27,000? Round your answer to one decimal place. Suppose that salaries for recent graduates of one university have a mean of $24,700 with a standard deviation of $1150.Example 1: Use Chebyshev’s Theorem to find what percentage of values will fall between 30 and 70 for a dataset with a mean of 50 and standard deviation of 10. First, determine the value for k. We can do this by finding out how many standard deviations away 30 and 70 are from the mean: (30 – mean) / standard deviation = (30 – 50) / 10 ...Chebyshev's theorem is a useful mathematical theorem that works for any shaped distribution, making it a valuable tool for interpreting standard deviation. 📏 The symbols used in the picture represent the population mean (mu) and standard deviation (sigma), providing a visual understanding of their relationship. Apr 16, 2020 · Chebyshev’s Theorem states that for any number k greater than 1, at least 1 – 1/k 2 of the data values in any shaped distribution lie within k standard deviations of the mean. For example, for any shaped distribution at least 1 – 1/3 2 = 88.89% of the values in the distribution will lie within 3 standard deviations of the mean. Chebyshev's theorem is any of several theorems proven by Russian mathematician Pafnuty Chebyshev. Bertrand's postulate, that for every n there is a prime between n and 2 n. Chebyshev's inequality, on the range of standard deviations around the mean, in statistics. Chebyshev's sum inequality, about sums and products of decreasing sequences. In the probability theory the Chebyshev’s Inequality & central limit theorem deal with the situations where we want to find the probability distribution of sum of large numbers of random variables in approximately normal condition, Before looking the limit theorems we see some of the inequalities, which provides the bounds for the …Chebyshev’s Theorem Example. Suppose that Y is a random variable with mean and variance ˙2. Find an interval (a;b) | centered at and symmetric about the mean | so that P(a<Y <b) 0:5. Example Suppose, in the example above, that Y ˘N(0;1). Let (a;b) be the interval you computed. What is the actual value of P(a<Y <b) in this case? Example.Study with Quizlet and memorize flashcards containing terms like Empirical Rule: 1 standard deviation, Empirical Rule: 2 standard deviations, ...Gostaríamos de exibir a descriçãoaqui, mas o site que você está não nos permite.Statistics and Probability questions and answers. Select all that apply Which of the following is true regarding the application of Chebyshev's theorem and the Empirical Rule? Check all that apply. Chebyshev's theorem applies to any set of values. Chebyshev's theorem works for symmetrical, bell-shaped distributions.The mean price of new homes is $200,000 with a standard standard deviation of $6,000. Using Chebyshev's Theorem, find the minimum percent of homes within 3 standard deviations of the mean. Chebyshev’s inequality is an extremely useful theorem when combining with other theorem and it is a bedrock of confidence interval. In this blog, I will illustrate the theorem and how it works ...Apr 19, 2021 · Learn how to use Chebyshev's Theorem to estimate the minimum and maximum proportion of observations that fall within a specified number of standard deviations from the mean. The theorem applies to any probability distribution and provides helpful results when you have only the mean and standard deviation. Compare it with the Empirical Rule, which is limited to the normal distribution. Chebyshev's theorem is a useful mathematical theorem that works for any shaped distribution, making it a valuable tool for interpreting standard deviation. 📏 The symbols used in the picture represent the population mean (mu) and standard deviation (sigma), providing a visual understanding of their relationship. Diagram for proof of Chebyshev's theorem. Then, dividing the integral into three parts as shown in Figure 2, we get σ2 = ∫ μ−kσ. −q. (x−μ)2 · f(x) dx+.Math. Statistics and Probability. Statistics and Probability questions and answers. The mean income of a group of sample observations is $500; the standard deviation is $40. According to Chebyshev's theorem, at least what percent of the incomes will lie between $400 and 5600? Percent of the incomes.Problem Statement − Use Chebyshev's theorem to find what percent of the values will fall between 123 and 179 for a data set with mean of 151 and standard deviation of 14. …切比雪夫定理的这一推论，使我们关于算术平均值的法则有了理论根据．设测量某一物理量a，在条件不变的情况下重复测量n次，得到的结果X 1 ，X 2 ，…，X n 是不完全相同的，这些测量结果可看作是n个独立随机变量X 1 ，X 2 ，…，X n 的试验数值，并且有同一数学期望a。 。于是，按大数定理j可知 ...Chebyshev’s Theorem Formula: Chebyshev’s theorem formula helps to find the data values which are 1.5 standard deviations away from the mean. When we compute the values from Chebyshev’s formula 1- (1/k^2), we get the 2.5 standard deviation from the mean value. Chebyshev’s Theorem calculator allow you to enter the values of “k ... Subject classifications. Bertrand's postulate, also called the Bertrand-Chebyshev theorem or Chebyshev's theorem, states that if n>3, there is always at least one prime p between n and 2n-2. Equivalently, if n>1, then there is always at least one prime p such that n<p<2n. The conjecture was first made by Bertrand in 1845 (Bertrand 1845; Nagell ... 切比雪夫定理（Chebyshev's theorem）：适用于任何数据集，而不论数据的分布情况如何。 与平均数的距离在z个标准差之内的数值所占的比例至少为(1-1/z 2)，其中z是大于1的任意实数。. 至少75%的数据值与平均数的距离在z=2个标准差之内；To apply Chebyshev’s theorem, you need to choose a value for k, an integer greater than or equal to 1. This value represents the number of standard deviations away from the mean you want to analyze. 6. Applying Chebyshev’s theorem. Now that you have the mean, standard deviation, and k value, you can apply Chebyshev’s theorem to calculate ...Chebyshev’s Theorem or Chebyshev’s inequality, also called Bienaymé-Chebyshev inequality, is a theorem in probability theory that characterizes the dispersion of data away from its mean (average). Chebyshev’s inequality (named after Russian mathematician Pafnuty Chebyshev) puts an upper bound on the probability that an observation is at ...Chebyshev’s inequality is a probability theory that guarantees only a definite fraction of values will be found within a specific distance from the mean of a distribution. The fraction for which no more than a certain number of values can exceed is represented by 1/K2. Chebyshev’s inequality can be applied to a wide range of distributions ... 切比雪夫不等式（英語： Chebyshev's Inequality ），是概率论中的一个不等式，顯示了隨機變量的「幾乎所有」值都會「接近」平均。 在20世纪30年代至40年代刊行的书中，其被称为比奈梅不等式（ Bienaymé Inequality ）或比奈梅-切比雪夫不等 …Use Chebyshev's theorem to determine the percentage of the data within each of the following ranges (to the nearest whole number). 20 to 40, at least % 15 to 45, at least % 22 to 38, at least % 18 to 42, at least % 12 to 48, at least % Consider a sample with a mean of 30 and a standard deviation of 5.The theorems 1)–8) on the distribution of prime numbers, proved by P.L. Chebyshev ... By now (1987) Chebyshev's theorems have been superceded by better results. E.g., $$\pi(x)=\operatorname{li}(x)+O(x\exp(-c\sqrt{\log x}))$$ (see for even better results); further $\pi(x)-\operatorname{li}(x)$ changes sign infinitely often.But we can have an idea of the importance of the theorem imagining all involved functions to be polynomials: that is, let’s imagine that in Chebyshev’s Theorem \pi (x) π(x) is a polynomial, and that in place of the function \frac {x} {\log x} logxx there is a polynomial, for example the second degree polynomial 2x^2 - 3x + 4 2x2 −3x+4.Sep 11, 2014 ... The situation for explicit integration in \eta is complementary to that in t. ... We also show that our method may be used to study more realistic ...In this video, we'll be discussing the empirical rule and Chebyshev's theorem. We'll also be discussing how they can be used to calculate probabilities.If yo...Proof of Chebyshev's theorem. (a) Show that ∫x 2 π(t) t2 dt =∑p≤x 1 p + o(1) ∼ log log x. ∫ 2 x π ( t) t 2 d t = ∑ p ≤ x 1 p + o ( 1) ∼ log log x. (b) Let ρ(x) ρ ( x) be the ratio of the two functions involved in the prime number theorem: Show that for no δ > 0 δ > 0 is there a T = T(δ) T = T ( δ) such that ρ(x) > 1 ... The rule is often called Chebyshev's theorem, about the range of standard deviations around the mean, in statistics. The inequality has great utility ...To apply Chebyshev’s theorem, you need to choose a value for k, an integer greater than or equal to 1. This value represents the number of standard deviations away from the mean you want to analyze. 6. Applying Chebyshev’s theorem. Now that you have the mean, standard deviation, and k value, you can apply Chebyshev’s theorem to calculate ...Question: Chebyshev's theorem is applicable when the data are Multiple Choice Ο any shape Ο skewed to the left Ο skewed to the right Ο approximately symmetric and bell-shaped. Show transcribed image text. There are 2 steps to solve this one.19.2 Chebyshev’s Theorem We’ve seen that Markov’s Theorem can give a better bound when applied to Rb rather than R. More generally, a good trick for getting stronger bounds on a ran-dom variable R out of Markov’s Theorem is to apply the theorem to some cleverly chosen function of R. Choosing functions that are powers of the absolute ...Chebyshev's inequality approximation for one sided case. Hot Network Questions How should I reconcile the concept of "no means no" when I tease my 5-year-old during tickle play? why stabilator has a lower travel limit for down movements? Why is post exposure vaccines given for some diseases & why does it work? ...Jul 21, 2011 ... Example: Imagine a dataset with a nonnormal distribution, I need to be able to use Chebyshev's inequality theorem to assign NA values to any ...Proof of Chebyshev's theorem. (a) Show that ∫x 2 π(t) t2 dt =∑p≤x 1 p + o(1) ∼ log log x. ∫ 2 x π ( t) t 2 d t = ∑ p ≤ x 1 p + o ( 1) ∼ log log x. (b) Let ρ(x) ρ ( x) be the ratio of the two functions involved in the prime number theorem: Show that for no δ > 0 δ > 0 is there a T = T(δ) T = T ( δ) such that ρ(x) > 1 ... this theorem in 1875 and Chebychev in 1878, both using completely different approaches [1]. Figure 1: Three different four-bar linkages tracing an identical coupler curve.This is a brief video concerning the premises of Chebyshev's Theorem, and how it is used in practical applications.Jan 20, 2019 · So Chebyshev’s inequality says that at least 89% of the data values of any distribution must be within three standard deviations of the mean. For K = 4 we have 1 – 1/K 2 = 1 - 1/16 = 15/16 = 93.75%. So Chebyshev’s inequality says that at least 93.75% of the data values of any distribution must be within two standard deviations of the mean. Chebyshev's Theorem. The Russian mathematician P. L. Chebyshev (1821- 1894) discovered that the fraction of observations falling between two distinct values, whose differences from the mean have the same absolute value, is related to the variance of the population. Chebyshev's Theorem gives a conservative estimate to the above percentage.Apr 16, 2020 ... How to Apply Chebyshev's Theorem in Excel. Chebyshev's Theorem states that for any number k greater than 1, at least 1 – 1/k2 of the data values ...This theorem makes rigorous the intuitive notion of probability as the expected long-run relative frequency of an event's occurrence. It is a special case of any of several more general laws of large numbers in probability theory. Chebyshev's inequality. Let X be a random variable with finite expected value μ and finite non-zero variance σ 2.Chebyshev's theorem applies to all data sets, whereas the empirical rule is only appropriate when the data have approximately a symmetric and bell-shaped distribution. The Sharpe ratio measures the extra reward per unit of risk This article deals with investigations by Pafnuty Chebyshev and Samuel Roberts in the late 1800s, which led them independently to the conclusion that for each curve that can be drawn by four bar linkages, there are always three linkages describing the same curve. These different linkages resulting in the same curve can be called cognate linkages.Question: Time Spent Online Americans spend an average of 3 hours per day online. If the standard deviation is 37 minutes, find the range in which at least 88.89% of the data will lie. Use Chebyshev's theorem. Round your k to the nearest whole number. At least 88.89% of the data will lie between and minutes. There are 3 steps to solve this one.The reason that the Chebyshev's Theorem would be used instad of the Empirical Rule is that Chebyshev's Theorem is valid for any set of data. Where any set of data within the K standard deviations of the mean is demonstrated 1-1/K², K being any number greater than 1. Example: When K = 2 the formula will demonstrate that 75% of the data will ...Chebyshev’s Theorem Formula: Chebyshev’s theorem formula helps to find the data values which are 1.5 standard deviations away from the mean. When we compute the values from Chebyshev’s formula 1- (1/k^2), we get the 2.5 standard deviation from the mean value. Chebyshev’s Theorem calculator allow you to enter the values of “k ... Learn how to apply Chebyshev's theorem to estimate the proportion of values falling within or beyond a certain range of the mean. See examples of …
Chebyshev’s Theorem Multiple Choice. applies to all samples. applies only to samples from a normal population. gives a narrower range of predictions than the Empirical Rule. is based on Sturges’ Rule for data classification. There’s just one step to solve this.. Redbox rental movies
This is just a few minutes of a complete course. Get full lessons & more subjects at: http://www.MathTutorDVD.com.You will learn about Chebyshev's Theorem in...Jun 28, 2015 · This theorem was proved by P.L. Chebyshev in 1854 (cf. [1]) in a more general form, namely for the best uniform approximation of functions by rational functions with fixed degrees of the numerator and denominator. Chebyshev's theorem remains valid if instead of algebraic polynomials one considers polynomials. where $\ {\phi_k (x)\}_ {k=0}^n$ is ... In this video I cover at little bit of what Chebyshev's theorem says, and how to use it. Remember that Chebyshev's theorem can be used with any distribution...28K views 3 years ago Introduction To Elementary Statistics Videos. In this video we discuss what is, and how to use Chebyshev's theorem and the empirical rule …Diagram for proof of Chebyshev's theorem. Then, dividing the integral into three parts as shown in Figure 2, we get σ2 = ∫ μ−kσ. −q. (x−μ)2 · f(x) dx+.Using Chebyshev's theorem, calculate the minimum proportions of computers that fall within 2 standard deviations of the mean. Step 1: Calculate the mean and standard deviation. The mean of the ... WP.2.4: CHEBYSHEV'S THEOREM & THE EMPIRICAL RULE · At least 75% of the data is within 2 standard deviations of the mean. · At least 89% of the data is within ...Pafnuty Lvovich Chebyshev (Russian: Пафну́тий Льво́вич Чебышёв, IPA: [pɐfˈnutʲɪj ˈlʲvovʲɪtɕ tɕɪbɨˈʂof]) (16 May [O.S. 4 May] 1821 – 8 December [O.S. 26 November] 1894) was a Russian mathematician and considered to be the founding father of Russian mathematics.. Chebyshev is known for his fundamental contributions to the fields of probability, statistics ...Jan 12, 2011 ... 3 Answers 3 ... So P(|X−μ|≥kσ)≤1k2. The central 60% is 1−P(|X−μ|≤kσ)=0.4. ... This is the one that says the probability of being outside k ...Feb 7, 2024 · Using Chebyshev’s Theorem, at least what percentage of adults have a score between 55 and 145? Problem 6: The mean weight of a package handled by Speedy Delivery Inc. is 18 lbs with a standard deviation of 7 lbs. Using Chebyshev’s Theorem, at least what percentage of packages will lie within 2 standard deviations of the mean? Chebyshev’s Theorem, also known as Chebyshev’s Rule, states that in any probability distribution, the proportion of outcomes that lie within k standard deviations from the mean is at least 1 – 1/k², for any k …This lecture will explain Chebyshev's inequality with several solved examples. A simple way to solve the problem is explained.Other videos @DrHarishGarg Cheb...What I am looking to figure out is this: For chebyshev's theorem to find an interval centered about the mean for the annual nunber of storms you would expect at least 75% of the years. Total of 20 years reported. Mean number of storms is 730 and the standard sample deviation is 172.Diagram for proof of Chebyshev's theorem. Then, dividing the integral into three parts as shown in Figure 2, we get σ2 = ∫ μ−kσ. −q. (x−μ)2 · f(x) dx+.Chebyshev's Interval refers to the intervals you want to find when using the theorem. For example, your interval might be from -2 to 2 standard deviations from the mean. Chebyshev's inequality, also known as Chebyshev's theorem, makes a fairly broad but useful statement about data dispersion for almost any data distribution.Chebyshev's theorem is any of several theorems proven by Russian mathematician Pafnuty Chebyshev. Bertrand's postulate, that for every n there is a prime between n and 2 n. Chebyshev's inequality, on the range of standard deviations around the mean, in statistics. Chebyshev's sum inequality, about sums and products of decreasing sequences. Chebyshev's Theorem: Let X X be a discrete random variable with finite mean μx μ x and standard deviation σx σ x. Let k k be greater than 1 1. Then the probability that X X is more than k k standard deviations from the mean, μX μ ….