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Math Help - Geometric random variable

  1. #1
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    Geometric random variable

    Let X be a random variable with distribution function px(x) defined by:

    px(0) = a and px(x) = Px(-x) = ((1-a)/2) * p * (1-p)^(x-1) x = 1,2...

    where a and p are two constants between 0 and 1.

    a) What is the mean of X?
    b) Use the variance of a geometric random variable to compute the variance of X.

    Okay so for a) I just used the geometric random variable formula, but made ((1-a)/2) = b. Since the mean of a geometric random variable with probability of success p is E(X) = 1/p, I just multiplied it by b, giving me -(a-1)/2p. Is this correct? If it is correct then I'm pretty sure I know how to do part b), so if anyone could help me with this I'd really appreciate it.

    Thanks in advance.
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  2. #2
    MHF Contributor matheagle's Avatar
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    what does px(0) = a and px(x) = Px(-x) mean?

    Is px(0) the probability that X=0?
    and is this symmetric about 0, with the px(x) = Px(-x)?
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  3. #3
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    Quote Originally Posted by matheagle View Post
    what does px(0) = a and px(x) = Px(-x) mean?

    Is px(0) the probability that X=0?
    and is this symmetric about 0, with the px(x) = Px(-x)?
    Yup, px(0) is meant to be that the probability that X=0, and I *think* it is meant to be symmetric about 0 (with px(x) = Px(-x)). Do they play some part in the mean of X? (I didn't really take them into account when I tried to work out the mean because I didn't think they were important...).
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