A month of the year is chosen at random (each with probability 1/12 ),Let X be the number of letters in the month's name, and let Y be the number of days in the month (ignoring leap year).

(a) Write down the joint probability density function (pdf) of X and Y, From this, compute the marginal of X and the marginal of Y (4 marks)

(b) Find E(Y)(2 marks)

(c) Are the eventsX6

X6and Y = 30 independent?(2 marks)

(d) Are X and Y independent random variables? (2 marks)