2. Prove that if random variable X follows a standard normal distribution (with mean ? = 0 and s

Name: 2. Prove that if random variable X follows a standard normal distribution (with mean ? = 0 and standard deviation ? = 1), then Y = X^2 follows a chi-square distribution with 1 degree of freedom. In particular, show that MY(t) = MX^2(t) ? E[e^tX^2], which equals the moment generating function of a chi-square distribution with 1 degree of freedom.
Uploaded: 2023-02-25T11:09:23-08:00
Duration: 1 min 30 s
Channel: Sri K
Description: 2. Prove that if random variable X follows a standard normal distribution (with mean ? = 0 and standard deviation ? = 1), then Y = X^2 follows a chi-square distribution with 1 degree of freedom. In particular, show that MY(t) = MX^2(t) ? E[e^tX^2], which equals the moment generating function of a chi-square distribution with 1 degree of freedom.

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Keondre Parker · Accepted Answer

1. We know that the probability density function (pdf) of a standard normal distribution is give

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