An two engine plan is capable of flying as long as one engine isrunning. Let the right and left engines be X and Y randomvariables that are independent. Denote the densities for Xand Y as fX and fY , and the distributions are FX(x) and FY(y). Let thecrash time of the plane be random variableZ=max(X,Y). Find the density function fZ(z) that describes Z. "Hint: for the algebraic variable z, express the event {max(X,Y)<=z) in terms of the events {X<=z} and{Y<=z}".