Marc leaves his office every day at a random time between 5:00 pm and 5:10 pm.If he leaves t minutes past 5:00pm,the time it takes him to reach home is a random number of minutes between 30 and 30+t^2.Let Y be the number of minutes past 5:00 pm that Marc leaves his office tomorrow, and let X be the number of minutes it takes him to reach home. (We assume Y takes any real value, e.g.,Y =3.14159 is possible).

(a) What is the expected length of time it takes him to reach home
(b) Find the joint probability density function of X and Y