# Question

What is the smallest value of k in Chebyshev’s theo-rem for which the probability that a random variable will take on a value between µ – kσ and µ+ kσ is

(a) At least 0.95;

(b) At least 0.99?

(a) At least 0.95;

(b) At least 0.99?

## Answer to relevant Questions

If we let kσ = c in Chebyshev’s theorem, what does this theorem assert about the probability that a random variable will take on a value between µ – c and µ+ c? With reference to Exercise 4.37, find the variance of the random variable by In exercise (a) Expanding the moment-generating function as an infinite series and reading off the necessary coefficients; (b) Using Theorem 4.9. If X and Y have the joint probability distribution f(–1, 0) = 0, f(–1, 1) = 14 , f(0, 0) = 16 , f(0, 1) = 0, f(1, 0) = 1 12 , and f(1, 1) = 12 , show that (a) cov(X, Y) = 0; (b) The two random variables are not ...With reference to Example 3.22 on page 94, and part (b) of Exercise 3.78 on page 100, find the expected value of X22X3 given X1 = 1/2. Find the expected value of the random variable Y whose probability density is given byPost your question

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