In a solution I am trying to understand, we are given:
And then the next step is written as:
Can someone please explain to me how this step is made? I can see why the mean would be zero, but why are the variances summed? Thank you.
In a solution I am trying to understand, we are given:
And then the next step is written as:
Can someone please explain to me how this step is made? I can see why the mean would be zero, but why are the variances summed? Thank you.
I assume A and B are independent.
So you want a difference of two normal random variables to have a variance of zero. Which would mean no uncertainty at all in the value of A - B .......
It can be proved that if then:
.
If and are independent then .
Property 2 here: http://en.wikipedia.org/wiki/Normal_distribution
is of related interest.