Two variables X and Yare defined as normal random variables such that X-N(200,5^20) and Y-N(180,4^2). Find the expectation and variance for the variables A and B when. A=X+Y and B=X-Y
The expectation operator is linear, so:
which gives the expectation of and straight off.
Now there is an equivalent result for variances but here I will be more long winded:
you know from the earlier part of this post, and:
but as and are independant , and of course:
and similarly for
CB