Let X denote the temperature (degree C) and let Y denote thetime in minutes that it takes for the diesel engine on anautomobile to get ready to start. Assume that the joint density for(X, Y) is given by fxy (x, y) = c(4x + 2y +1) ; 0 < x< 40 and 0 < y <2.
(a) Find the value of c that makes this a density.
(b) Find the probability that on a randomly selected day theair temperature will exceed 20 degrees C and it will take at least1 minute for the car to be ready to start.
(c) Find the marginal densities for X and Y.
(d) Find the probability that on a randomly selected day itwill take at least one minute for the car to be ready tostart.
(e) Find the probability that on a randomly selected day theair temperature will exceed 20 degrees C.
(f) Are X and Y independent? Explain on mathematicallybasis.