The sum of n independent Geometric random variables is a geometric distribution with alpha equal to which value?

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Multiple Choice

The sum of n independent Geometric random variables is a geometric distribution with alpha equal to which value?

When you add independent geometric random variables, the result is a negative binomial distribution. In that family, the parameter alpha counts how many geometric terms were combined (the number of successes you’re aiming for). Since you summed n geometric variables, the negative binomial distribution has alpha equal to n. The pmf can be written as P(S = k) = C(k + n − 1, k) (1 − p)^k p^n for k = 0, 1, 2, ..., where p is the common success probability of each geometric variable. So alpha = n.

When you add independent geometric random variables, the result is a negative binomial distribution. In that family, the parameter alpha counts how many geometric terms were combined (the number of successes you’re aiming for). Since you summed n geometric variables, the negative binomial distribution has alpha equal to n. The pmf can be written as P(S = k) = C(k + n − 1, k) (1 − p)^k p^n for k = 0, 1, 2, ..., where p is the common success probability of each geometric variable. So alpha = n.

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