Compute the hazard rate function of a gamma random variable with parameters (α, λ) and show it is increasing when α ≥ 1 and decreasing when α ≤ 1.
Answer to relevant QuestionsLet 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. Use the result that, for a nonnegative random variable Y, to show that, for a nonnegative random variable X, and make the change of variables t = xn. Two points are selected randomly on a line of length L so as to be on opposite sides of the midpoint of the line. [In other words, the two points X and Y are independent random variables such that X is uniformly distributed ...Suppose that A, B, C, are independent random variables, each being uniformly distributed over (0, 1). (a) What is the joint cumulative distribution function of A, B, C? (b) What is the probability that all of the roots of ...In Problem 3, calculate the conditional probability mass function of Y1 given that (a) Y2 = 1; (b) Y2 = 0. Problem 3 In Problem 2, suppose that the white balls are numbered, and let Yi equal 1 if the ith white ball is ...
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