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Math Help - joint pmf covariance

  1. #1
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    joint pmf covariance

    I have a joint p.m.f. but am very stuck with how to find the following:
    1) covariance
    2) correlation coefficient of X and Y
    3) If X and Y are independent

    I already calculated the marginal p.m.f.s, means and variances from my data which is as follows:


    x__ 1___ 2___ 3___ 4___ 5
    y
    3__.02_ .03_ .06__ .15_ .07
    2__.02_ .05_ .08__ .12_ .06
    1__.05_ .05_ .06__ .13_ .05
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  2. #2
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    Quote Originally Posted by antman View Post
    I have a joint p.m.f. but am very stuck with how to find the following:
    1) covariance
    2) correlation coefficient of X and Y
    3) If X and Y are independent

    I already calculated the marginal p.m.f.s, means and variances from my data which is as follows:


    x__ 1___ 2___ 3___ 4___ 5
    y
    3__.02_ .03_ .06__ .15_ .07
    2__.02_ .05_ .08__ .12_ .06
    1__.05_ .05_ .06__ .13_ .05
    1) If you know to compute mean of a random variable, covariance is not too hard. Covariance(X,Y) = E(XY) - E(X)E(Y). Thus first compute the mean of the product random variable XY

    2) \text{Correlation} = \frac{Cov(X,Y)}{\sqrt{\text{Var}(X)\text{Var}(Y)}}

    3) If Covariance is non -zero, the random variables are definitely not independent
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  3. #3
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    I know how to find E(X) and E(Y), the means 3.45 and 1.99 respectively, but how do I find E(XY)? Thank you for your help!
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  4. #4
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    I think I figured it out. I got covariance=7.01-3.45(1.99)=0.1445? Therefore, x and y are not independent. Is this correct?
    Also, how do I find the least squares regression line?

    Thank you!
    Last edited by antman; May 17th 2009 at 01:21 PM.
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