Problem #2 (20 points) - An Independent Sum a.) (10 points) Suppose that X, is uniform with Rx, = {1, 2,3, ., n} and X2 is geometric with parameter...
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Need help with part a) and b).

hmk_6_prob2.jpg

Problem #2 (20 points) - An Independent Sum
a.) (10 points) Suppose that X, is uniform with Rx, = {1, 2,3, ..., n} and X2
is geometric with parameter p. Determine the pmf for the sum X = X1+ X2
given that X1 and X2 are independent random variables. Hint: Once again,
you may use the fact that
1-r
for
r #1.
b.) (10 points) Now suppose that a fair die is rolled and a fair coin is flipped
until the first head occurs, and the number shown on the die plus the number
of flips is recorded. Compute the probability that this number is I = 8.

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