Expected value and variance of these sums

[Dixanadu]

Hi guys,

Suppose I have the function
$x = a + b -1$
where a, b have expected values of 0.5 each. What is the expected value of x? is it 0.5 + 0.5 -1 = 0? or is it just 0.5 + 0.5?

Secondly, suppose the same equation as above, $x = a + b -1$. If the variance of both a and b is 1/12, what is the variance of x?

I know this is really basic but I just don't understand. Thanks guys!

 

[mathman]

The expected value of x is 0, as you should expect. The expected value of a constant is its value.

If a and b are independent, the the variances just add, so the variance of x is 1/6. Note that the variance of a constant is 0.

 

[Dixanadu]

Okay, thank you :)