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    Probability: Joint Probability Mass Function, Covariance and Variance

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    Let X and Y have joint probability mass function Pr{X = i, Y = j}= c(i + 1)(j + 2) for
    i >= 0, j >= 0, and i + j < 4. Determine
    a) the marginal probability mass function of X
    b) the probability mass function of Y
    c) the conditional probability mass function of X given Y = 0
    d) the probability mass function of Z = X + Y
    e) the conditional probability mass function of Z given X = 0
    f) the mean of X
    g) the expected value of Y
    h) the mean of Z
    i) the variance of X
    j) the variance of Y
    k) the variance of Z
    l) the mean of XY
    m) the covariance of X and Y
    n) the mean of X conditioned on Y=0

    © BrainMass Inc. brainmass.com March 4, 2021, 5:45 pm ad1c9bdddf
    https://brainmass.com/math/probability/probability-joint-probability-mass-function-covariance-and-variance-9843

    Solution Summary

    Fourteen statistical quantities are calculatd from a joint probability mass function. The solution is detailed and well presented.

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