Let X be a uniformly distributed random variable on the interval [1, 1]. To find the density of Y = X^k, where k is a positive integer, differentiate between whether k is odd or even. Use the method from class of finding the density of a transformation of a random variable to determine the density of Y.

1. Let X be uniformly distributed on [ 1 , 1 ] . Find the density of Y = X k for positive integers k .
Hint : differentiate the cases k odd/even and use the same method as we did in class for the case
X 2 where X was a normal random variable, using the formula for the density of a tranformation
of a random variable