6.7 Suppose that Z has a standard normal distribution. a Find the density function of U = Z². b Does U have a gamma distribution? What are the values of a and B? c What is another name for the distribution of U?

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6.7 Suppose that Z has a standard normal distribution.
a Find the density function of U = Z².
b Does U have a gamma distribution? What are the values of a and B?
c What is another name for the distribution of U?
Transcribed Image Text:6.7 Suppose that Z has a standard normal distribution. a Find the density function of U = Z². b Does U have a gamma distribution? What are the values of a and B? c What is another name for the distribution of U?
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Step 1

Given that Z has a standard normal distribution.

The pdf of Z is

fZ(z)=12πe-z22, -<z<.

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