A genetic experiment on cell division can give rise to at most 2k cells,

and the probability function describing the variation in the number of

cells recorded is assumed to be

p(x) = x(1 -theta)/1-theta^(2k+1)

x = 0, 1, 2, ..., 2k

where 0 < theta < 1:

(b) Two independent replicates of the experiment are performed. What

are the probabilities

ii. that the number of cells produced in the two replicates are

the same;

iii. That the total number of cells produced from the two replicates

is exactly y, for 0 y 2k?