Thread: expected value help

Whats a hint to solve E(min(X,100)), when X~Geometric(theta)?

Originally Posted by Sneaky

Whats a hint to solve E(min(X,100)), when X~Geometric(theta)?

Review order statistics for geometric random variables.

E(min(X,100)) can be expanded into

99
summation y*theta*(1-theta)^y
y=o

+

inf.
summation 100*theta*(1-theta)^100
y=100

But I don't know what to do here.

Originally Posted by Sneaky

Whats a hint to solve E(min(X,100)), when X~Geometric(theta)?

I work in order stats and I don't know what that means.
Is it the smallest order stat from a sample of 100?

this question means
find the expected value of Z when Z is a function of the smaller value of X or 100, and X is a geometric distribution with expected value of theta.