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Math Help - PMF of random variable

  1. #1
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    PMF of random variable

    Ok so I have a PMF of X:

    P_X(x) = x^2/a for  x = -3, -2, -1, 0, 1, 2, 3,
                0, otherwise.

    (sorry - I don't really know how to write the PMFs on here but that was my best attempt)

    we had to work out a which I have as 28, and then E[X] which I got to be 0.

    However now I have to work out the PMF of Y if Y = (X - E[X])^2

    I really don't know how to approach this! I know it's something really simple but I can't think how I would do this!

    I know that as the expectation is 0, Y = X^2
    but from there I am unsure of how to get the PMF.
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  2. #2
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    Re: PMF of random variable

    Re-looking at this I think that a = 7x^2
    but assurance would be lovely!!!
    Not that anyone is actually looking at this but yeah....
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  3. #3
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    Re: PMF of random variable

    Quote Originally Posted by Natalie11391 View Post
    Re-looking at this I think that a = 7x^2
    but assurance would be lovely!!!
    Not that anyone is actually looking at this but yeah....
    You have to solve \frac{9}{a} + \frac{4}{a} + \frac{1}{a} + 0 + \frac{1}{a} + \frac{4}{a} + \frac{9}{a} = 1 for a.

    So your original answer of a = 28 is correct. I don't know why you have said a = 7x^2.
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  4. #4
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    Re: PMF of random variable

    Quote Originally Posted by Natalie11391 View Post
    Ok so I have a PMF of X:

    P_X(x) = x^2/a for  x = -3, -2, -1, 0, 1, 2, 3,
                0, otherwise.

    (sorry - I don't really know how to write the PMFs on here but that was my best attempt)

    we had to work out a which I have as 28, and then E[X] which I got to be 0.

    However now I have to work out the PMF of Y if Y = (X - E[X])^2

    I really don't know how to approach this! I know it's something really simple but I can't think how I would do this!

    I know that as the expectation is 0, Y = X^2
    but from there I am unsure of how to get the PMF.
    The sample space for Y is \{0,1,4,9\}, now use the PMF of X to evaluate the probability that Y takes each of these values.

    CB
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    Re: PMF of random variable

    I was just about to delete this because I eventually figured it out but thank you for helping anyway

    I thought it would be 7x^2 because a friend told me that he got that and that 28 was wrong but yeah, it turns out I WAS right originally!

    Thanks guys
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  6. #6
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    Re: PMF of random variable

    Quote Originally Posted by Natalie11391 View Post
    I was just about to delete this because I eventually figured it out but thank you for helping anyway

    [snip]
    Memo to all members: Don't delete posts. See the rules.
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  7. #7
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    Re: PMF of random variable

    oo ok!! Well I wasn't going to seeing as it now has replies but if something doesn't have any replies and it's been up for a while, can you still not delete it?
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