(Change of measure for an exponential random variable) Let X be a nonnegative random variable defined on a probability space (,F,P) with the exponential distribution, which is P{Xa}=1ea,a0 where is a positive constant. Let ~ be another positive constant, and define Z=~e(~)X Define P by P(A)=AZdPforallAF. (a) Show that P()=1. (b) Compute the cumulative distribution function P{Xa}fora0 for the random vatiable X under the probability measure P