(Solved):   Q1. Random variables X and Y are independent and uniformly distributed in [0,1]. Find the ...

 

Q1. Random variables X and Y are independent and uniformly distributed in [0,1]. Find the pdf f? (2) of the random variable X Z= y² +1 using the auxiliary variable method. Define an auxiliary variable Was a function of X and Y. (Hint: Define Win the simplest possible form. You should determine the region on the (z,w) plane in which the joint pdf of Z and Wis nonzero, by using the ranges in which X and Yare nonzero).