Computing the Mean of a Geometric Distribution

[shawn26]

Homework Statement

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 innite sum remaining.

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

 

[kai_sikorski]

hi shawn,

Welcome to the forums.

You need to show an attempt at a solution before we can help you.

 

[shawn26]

kinda how no clue how to go about it let me think about it a little more and get back