1. Let X follow a binomial distribution. Show that Var[X] < E[X].2. Suppose X follows a binomial distribution with mean 8 and variance 1.6.(a) Find the values of n and p.(b) Find P(X > 8).3. Suppose X follows a binomial distribution with parameters n and p. Let Y = n – X. Showthat Y is a binomial distribution with parameters n and 1-p. (To help think about it, thinkof X as the number of successes and Y is the number of failures.)

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1. Let X follow a binomial distribution. Show that Var[X]

A First Course in Probability (10th Edition)

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Question

1. Let X follow a binomial distribution. Show that Var[X] < E[X].
2. Suppose X follows a binomial distribution with mean 8 and variance 1.6.
(a) Find the values of n and p.
(b) Find P(X > 8).
3. Suppose X follows a binomial distribution with parameters n and p. Let Y = n – X. Show
that Y is a binomial distribution with parameters n and 1-p. (To help think about it, think
of X as the number of successes and Y is the number of failures.)

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