Question

Let X be a continuous random variable with the following PDF:

fX (x)={ 7 (1-x)⁶ 0{ 0 otherwise
Define Y=(1-X)⁶. Find the PDF of the random variable Y.

Answer 1

To find the PDF of the random variable Y, we need to find the distribution function of Y and differentiate it with respect to Y. The PDF of the random variable Y is fY(y) = 7(1-(1-y^(1/6)))⁶ * (1/6)(y^(-5/6)).

Step-by-step explanation:

To find the PDF of the random variable Y, we need to find the distribution function of Y and differentiate it with respect to Y.

Since Y=(1-X)⁶, we can find the distribution function of Y by substituting (1-X)⁶ into the given PDF of X:

fY(y) = fX(1-y^(1/6)) * (1/6)(y^(-5/6)), where 0 < y < 1.

Therefore, the PDF of the random variable Y is fY(y) = 7(1-(1-y^(1/6)))⁶ * (1/6)(y^(-5/6)).