Let X be a random variable that is exponentially distributed with A>0, i.e., fX(x) = A*exp(-Ax), for x>=0; and fX(x)=0, for x<0. (a) Define Y=[X], which is the integer part of X. Find the PMF {P(Y=k)}k for Y as an explicit function of A and k, check that it is a valid PMF. (b) Let Z=X-[X], which is the remainder of X after subtracting its integer part. For z = [0,1] express FZ(z) as an explicit function of A and z. Find the pdf fZ(z), check that it is a valid pdf.