A random variable X has three, and only three, possible values, 0; 2; 4
with the following probability distribution:
Getting a 0 is 0:7
Getting a 2 is 0:1
Getting a 4 is 0:2
Let X1 and X2 be two independent random variables with this distribution.
(a) Determine the probability distribution for
X(bar)2 = (X1 + X2)/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.
The Attempt at a Solution
X2(bar) = 0 with probability 0.49
X2(bar) = 1 with probability 0.14
X2(bar) = 2 with probability 0.29
X2(bar) = 3 with probability 0.04
X2(bar) = 4 with probability 0.04
not sure how to work out the variance?
Regards as always