Question: Let be a positive number. The continuous random variable X is called exponential with parameter when its probability density function is (a) Find

Let λ be a positive number. The continuous random variable X is called exponential with parameter λ when its probability density function is

Let λ be a positive number. The continuous random variable X is

(a) Find the cumulative distribution function (CDF) of X.

(b) Find the mean of X.

(c) Find the variance of X.

(d) Suppose X1, X2, and X3 are independent exponential random variables, each with parameter λ. Find the PDF of Z = max{X1, X2, X3}.

(e) Find the PDF of W = min{X1, X2}.

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