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## Homework Statement

A random variable has a distribution function F(z) given by

F(z) = 0 if z< -1

F(z) = 1/2 if -1 <= z < 2

F(z) = (1-z^{-3}) is 2 <= z

Find the associated mean and variance.

## The Attempt at a Solution

I drew the distribution function. I started with the associated mean (if I can figure that out the variance should follow.) I have:

E[Z] = [tex] \sum [/tex] zp(z)

p(z) = P[X = z]

Therefore,

p[X = -1] = P[X= -1] - P[X<-1]

= F(-1) - lim F(1-1/n)

= 1/2 - (1-2)

= 3/2

Sorry, if I messed up badly somewhere. The class is taught without a book and I can't seem to get anything out of my notes for this homework. Thanks.

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