# Question: If X has hazard rate function X t compute the hazard

If X has hazard rate function λX(t), compute the hazard rate function of aX where a is a positive constant.

## Relevant Questions

If X is an exponential random variable with mean 1/λ, show that E[Xk] = k! / λk k = 1, 2, . . . Let Y = (X – ν/α)β Show that if X is a Weibull random variable with parameters ν, α, and β, then Y is an exponential random variable with parameter λ = 1 and vice versa. Show that Z is a standard normal random variable, then, for x > 0, (a) P{Z > x} = P{Z < −x}; (b) P{|Z| > x} = 2P{Z > x}; (c) P{|Z| < x} = 2P{Z < x} − 1. The joint density of X and Y is given by (a) Are X and Y independent? If, instead, f (x, y) were given by (b) Would X and Y be independent? In Problem 2, suppose that the white balls are numbered, and let Yi equal 1 if the ith white ball is selected and 0 otherwise. Find the joint probability mass function of (a) Y1, Y2; (b) Y1, Y2, Y3. Problem 2 Suppose that 3 ...Post your question