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Problem H-10. We will compute the mean of the geometric distribution. (Note: It's also possible to

compute E(X^2) and then Var(X) = E(X^2)−(E(X))^2 by steps similar to these.)

(a) Show that

E(X) = (k=1 to infinity summation symbol) (k *q^k−1* p)

where q = 1−p.

(b) Show that the above summation can be rewritten as follows:

E(X) = p* d/dq (k=1 to infinity summation symbol) q^k

(c) The sum in part (b) is a geometric series. Evaluate the geometric series; replace the sum in (b) by this value; and do the derivative d/dq. The final answer will be a quotient of polynomials involving p

and q; there will not be an innite sum remaining.

(d) Plug in q = 1−p and simplify to get the final answer.

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# Homework Help: Probability, please help

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