Let S be a discrete random variable that takes the value 1 with probabilities p...

Let S be a discrete random variable that takes the valu value I with probability p E ( O , 1 ) , and the value - I with probability 1 - p . Let & be a continuous random variable whose conditional distribution given S is as follows If S = 1 , then X is exponential with parameter a > O l . e . fx s ( 20 1 ) = for ac > 1 , then - X is exponential with parameter B > O , i . e . , fxis ( 20 - 1 ) = Be Bu , for a SO Note that S can be viewed as the " sign " of X . Let 2 8 1 . Give an expression for fx ( 2 ) . Enter your answer using standard notation ; type alpha for a beta for B . ) For a > O ( x (20 ) For 2 0 ( x (20 ) 2 . Give an expression for PIS ) , as a function of 2 . ( Enter your answer using standard notation type alpha for a beta for B . ) P ( S = 12 = 2 )