let Y be a discrete random variable with possible values {0,1,2,.....} and the following probability mass function: P(Y=0) = 4/5 and for k is an element of 1,2,3,....

P(Y=k) = 1/10.(2/3)^k

a) verify that the above is a probability mass function.

b) for k is an element of 1,2,3,..., find P(Y more than and equal to k | X is more than and equal to 1).