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

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- November 7th 2010, 12:02 PMSneakyexpected value help
Whats a hint to solve E(min(X,100)), when X~Geometric(theta)?

- November 7th 2010, 12:06 PMmr fantastic
- November 7th 2010, 12:22 PMSneaky
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. - November 7th 2010, 03:13 PMmatheagle
- November 7th 2010, 03:23 PMSneaky
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.