50 points

the discrete random variable x can take only the values 1, 2, 3, 4, 5 and 6. the probability distribution of x is
described by the following statements:
p(x= 1) = p(x=3) = p(x= 5) = a
p(x= 2) = p(x= 4) = p(x= 6) = b
a=3b
(a) find the values of a and b.
(b) draw up a probability distribution table for x.
(c) show that e(x)= 13/4
(d) show that var(x) = 137/48
(e) find the probability that the sum of two independent observations from this distribution is greater than 9.