1. Let X be an exponential random variable with parameter ? = 1, and let Y = log X. Find the pro

Name: 1. Let X be an exponential random variable with parameter ? = 1, and let Y = log X. Find the probability density function of Y. Hint: First, find the cumulative distribution function Fy(y) = P(Y ? y) = P(log X ? y) = P(X ? e^y). Next, obtain the density function fy(y) of Y via differentiation as fy(y) = d/dy Fy(y).
Uploaded: 2022-04-12T06:08:30-08:00
Duration: 5 min 34 s
Channel: Shaiju T
Description: 1. Let X be an exponential random variable with parameter ? = 1, and let Y = log X. Find the probability density function of Y. Hint: First, find the cumulative distribution function Fy(y) = P(Y ? y) = P(log X ? y) = P(X ? e^y). Next, obtain the density function fy(y) of Y via differentiation as fy(y) = d/dy Fy(y).

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Shaiju T · Accepted Answer

Step 1: Find the cumulative distribution function of Y, Fy(y) = P(Y < y) = P(log(X) < y) = P(X <

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