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Math Help - Var(X) where X = 0 80% of the time and X ~ Uniform(1,b) 20% of the time

  1. #1
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    Var(X) where X = 0 80% of the time and X ~ Uniform(1,b) 20% of the time

    I think the title says it all but I'll elaborate a little...

    We want to know the variance of a random variable X which is:
    - equal to zero 80% of the time
    - equal to a random variable that is ~ Uniform(1,b) the other 20% of the time.

    I have searched all over the internet for this answer and have come up donuts. Your help and even just insights would be greatly appreciated. Thanks!
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  2. #2
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    Can you post the exact problem (I'm assuming this is a paraphrasing).
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  3. #3
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    The question in the OP is a problem I need to solve for a project (not a problem out of a textbook) so there's no "problem" to refer to. I'll try to describe the question in the OP a little differently:

    Suppose X: S --> [0, 10] is a continuous random var defined on sample space S with pdf =

    Pr(X = 0) = 0.8
    Pr(X) = (1-p(0))/(b - a) = 0.2/10 for all X within (0, 10]

    Find Var(X).

    In other words, for X = 0, the pdf of X is given by a constant (namely 0) and for X within (0,10], the pdf of X is given by Uniform(0,10].

    I realize that I can simply use the Var(X) = E[(X-u)^2] formula to solve this but I'd like to make sure there's no analytical solution before I go that route.

    Worded more generally, the question is as follows: Is there an analytical solution to find the variance of a r.v. X with different pdfs for different values of X.

    Thanks!
    Last edited by ltdanp21; November 18th 2009 at 09:38 AM.
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