Problem 2: 5 points Let U and T be independent random variables such that U is uniformly distributed on the interval (0, 27) and T has an exponential distribution with parameter 1. Show that X = V2T cos(U), Y = V2T sin(U) are independent standard normal random variables.

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Problem 2: 5 points Let U and T be independent random variables such that U is uniformly
distributed on the interval (0, 27) and T has an exponential distribution with parameter 1.
Show that X = V2T cos(U), Y = V2T sin(U) are independent standard normal random
variables.
Transcribed Image Text:Problem 2: 5 points Let U and T be independent random variables such that U is uniformly distributed on the interval (0, 27) and T has an exponential distribution with parameter 1. Show that X = V2T cos(U), Y = V2T sin(U) are independent standard normal random variables.
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