(b) Suppose X is an Exponential random variable with rate > > 0, so that X...

Transcribed Image Text:

(b) Suppose X is an Exponential random variable with rate > > 0, so that X has probability density function fx(x) = SA exp \exp (-Ax) if x > 0, = otherwise. i. Calculate E(X) and Var(X). ii. Let X1, X2,..., X 100 be a sample of independent identically distributed copies of an Exponential random variable with rate 1. Calculate E(X) and Var(X), where X is the sample mean. iii. Use the Central Limit Theorem to find an approximate value for P(X > 1.234). (b) Suppose X is an Exponential random variable with rate > > 0, so that X has probability density function fx(x) = SA exp \exp (-Ax) if x > 0, = otherwise. i. Calculate E(X) and Var(X). ii. Let X1, X2,..., X 100 be a sample of independent identically distributed copies of an Exponential random variable with rate 1. Calculate E(X) and Var(X), where X is the sample mean. iii. Use the Central Limit Theorem to find an approximate value for P(X > 1.234).