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    A random variable R takes the integer value r with probability p(r), where:

    p(r) = kr^3 r = 1,2,3,4
    p(r) = 0 otherwise.

    Find

    a) the value of k, and display the distribution on graph paper.
    b) the mean and the variance of the distribution


    a)
    r: 1 2 3 4
    (R=r) 1k 8k 27k 64k


    1k + 8k + 27k + 64k = 1

    k( 1 + 8 +27 +64) = 1

    Therefore k = 1/100

    b) I worked out the mean to be 177/50 (which is correct) and tried to find the variance by trying to find E(R^2):

    r : 1 4 9 16
    R=r) : 1/100 8/100 27/100 64/100

    E(R^2) = (1 x 1/100) + (4 x 8/100) + ( 9 x 27/100) + (16 x 64/100)
    = 1300/100 = 650/50

    Variance = E (R^2) - Mean
    = 650/50 - 177/50
    = 473/50 (WRONG!)



    The answer I get doesn't match the answer in the book. Help please!
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    (Original post by Mambo No. 5)
    Variance = E (R^2) - Mean
    = 650/50 - 177/50
    = 473/50 (WRONG!)

    [/B][/COLOR]

    The answer I get doesn't match the answer in the book. Help please!
    The issue is that \text{Var}(X) = \text{E}(X^2) - [\text{E}(X)]^2. So you've just got the wrong formula for variance.

    Try what you did again, but this time square the mean.
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    (Original post by .ACS.)
    The issue is that \text{Var}(X) = \text{E}(X^2) - [\text{E}(X)]^2. So you've just got the wrong formula for variance.

    Try what you did again, but this time square the mean.
    Thank you! Got the right answer. +1rep.
 
 
 
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