# Question: Use the inequality of Exercise 4 29 to prove Cheby shev s theorem In

Use the inequality of Exercise 4.29 to prove Cheby-shev’s theorem.

In exercise

P(X ≥ a) ≤ µ / a

In exercise

P(X ≥ a) ≤ µ / a

## Answer to relevant Questions

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? Show that if a random variable has the probability density f(x) = 1/2 e–|x| for –∞ < x < ∞ Its moment-generating function is given by With reference to Exercise 3.74 on page 100, find cov( X, Y). With reference to Exercise 3.74 on page 100, find the conditional mean and the conditional variance of Y given X = 1/4. With reference to Exercise 3.101 on page 108, find E(PS), the expected receipts for the commodity.Post your question