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Math Help - Discrete Uniform Random Variable 2

  1. #1
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    Discrete Uniform Random Variable 2

    I have the question:

    Explain why a discrete uniform random variable, X, on [a,b] has the same variance as a discrete uniform random variable, W, on [1,b-a+1].

    Use this information to establish that



    ...I don't even know where to start so any help would be great cheers
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  2. #2
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    Quote Originally Posted by sirellwood View Post
    I have the question:

    Explain why a discrete uniform random variable, X, on [a,b] has the same variance as a discrete uniform random variable, W, on [1,b-a+1].

    Use this information to establish that



    ...I don't even know where to start so any help would be great cheers
    [a, b] --> [1, b - a + 1] suggests a horizontal translation of -a + 1: W = X - a + 1. And you should know that the shape of a distribution is unaffected by horizontal translation ....
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    ah ok, so you are saying that Var(X)=(b-a)*(b-a)/12. and Var(W)=(b-a)*(b-a)/12
    for the first one a=a, b=b; for the second one a=1, b=b-a+1; so...

    Var(X1)=Var(W)?
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  4. #4
    MHF Contributor matheagle's Avatar
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    V(aX+b)=a^2V(X)

    The b, is a shift and that only changes the mean (center) not the variance (spread).

    2b or not 2b? oh well it's 2am.
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