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## Homework Statement

A random variable X has three, and only three, possible values, 0; 2; 4

with the following probability distribution:

Probability:

Getting a 0 is 0:7

Getting a 2 is 0:1

Getting a 4 is 0:2

Let X

_{1}and X

_{2}be two independent random variables with this distribution.

(a) Determine the probability distribution for

X(bar)

_{2}= (X

_{1}+ X

_{2})/2

and use this distribution to determine the expectation and variance of X(bar)

_{2}

(b) Determine the expectation and variance of X and verify that the

variance of X(bar)

_{2}is one-half the variance of X.

## Homework Equations

## The Attempt at a Solution

X

_{2}(bar) = 0 with probability 0.49

X

_{2}(bar) = 1 with probability 0.14

X

_{2}(bar) = 2 with probability 0.29

X

_{2}(bar) = 3 with probability 0.04

X

_{2}(bar) = 4 with probability 0.04

not sure how to work out the variance?

Regards as always

Tam

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