Expected value and variance of these sums

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SUMMARY

The expected value of the function x = a + b - 1, where both a and b have expected values of 0.5, is definitively 0. This is calculated as 0.5 + 0.5 - 1 = 0. For the variance, given that both a and b have a variance of 1/12 and are independent, the variance of x is calculated by adding the variances, resulting in a variance of 1/6. The variance of a constant is 0, confirming that only the variances of a and b contribute to the variance of x.

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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!
 
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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.
 
Okay, thank you :)
 

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