question archive Let Xi ~ Exponential(B), 2 = 1, 2, 3 and assume they are independent
Let Xi ~ Exponential(B), 2 = 1, 2, 3 and assume they are independent
Subject:MathPrice: Bought3
Let Xi ~ Exponential(B), 2 = 1, 2, 3 and assume they are independent. Find p( Xitx2 < t) for t > 0. Hint: Use the multivariate transformation method to find the PDF of 12. You can also apply the results that were proved in previous Modules. 10 point
Hints: 1. U N Uniform(0,1), then — 111(U) ~ Exponential?). 2. If X N gamma.(a, )8), then (:X N gamma(a, 0,8), (3 > 0 3. If Xi ~ gamma(aé,,8),then 2:":1 X,; N gamma(z?=l (11;, [3), where Xhi = 1, 2, 3..., n are independent random variables.
