Question

Assume X ~ N(56,2) and Y = 14X2 / pi. What is the PDF
of Y?

Answer 1

To find the PDF of Y, we need to find the distribution of X^2 using the distribution of X, and then use the properties of transformation of random variables to determine that Y follows a scaled chi-squared distribution with one degree of freedom.

Step-by-step explanation:

To find the PDF of Y, we need to find the distribution of Y. First, we need to find the distribution of X^2 using the distribution of X. Since X ~ N(56,2), X^2 follows a chi-squared distribution with one degree of freedom.

Now, we can find the distribution of Y = 14X^2 / pi. Using the properties of transformation of random variables, we can determine that Y follows a scaled chi-squared distribution with one degree of freedom.