Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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


    User Avatar
    Science Advisor

    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 :)
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook