# Question

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.

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.

## Answer to relevant Questions

If X is a beta random variable with parameters a and b, show that E[X] = a/a + b Var(X) = ab/(a + b)2(a + b + 1) Let X be a random variable that takes on values between 0 and c. That is, P{0 ≤ X ≤ c} = 1. Show that Var(X) ≤ c2/4 One approach is to first argue that E[X2] ≤ cE[X] and then use this inequality to show that Var(X) ...Show that f (x, y) = 1/x, 0 < y < x < 1, is a joint density function. Assuming that f is the joint density function of X,Y, find (a) The marginal density of Y; (b) The marginal density of X; (c) E[X]; (d) E[Y]. If X1 and X2 are independent exponential random variables with respective parameters λ1 and λ2, find the distribution of Z = X1/X2. Also compute P{X1 < X2}. In Problem 5, calculate the conditional probability mass function of Y1 given that (a) Y2 = 1; (b) Y2 = 0. Problem 5 Repeat Problem 3a when the ball selected is replaced in the urn before the next selection. Problem 3 In ...Post your question

0