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Expected value and variance of these sums

  1. Nov 3, 2014 #1
    Hi guys,

    Suppose I have the function
    [itex]x = a + b -1[/itex]
    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, [itex]x = a + b -1[/itex]. 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 dont understand. Thanks guys!
     
  2. jcsd
  3. Nov 3, 2014 #2

    mathman

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    Science Advisor
    Gold Member

    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.
     
  4. Nov 4, 2014 #3
    Okay, thank you :)
     
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