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    Statistics: A Coin Toss

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    A fair coin is tossed 3 times. Let X be the number of heads on the third tossing and let Y be the total number of heads.

    a) Find the joint pdf of X and Y.
    b) Find the marginal pdf of X. Compute E(x) and V(x) - does X follow classical distribution?
    c) Find the marginal cdf of Y. Compute E(y) and V(y) - does Y follow classical distribution?
    d) Compute E(xy), Cov (XY) (covariance) and (rho) (greek letter p).
    e) Find all conditional pdf's of X given Y=y.
    f) Find all conditional pdf's of Y given X=x.
    g) Compute E(X|y) for possible values of y of Y.
    h) Compute E(Y|x) for possible values of x of X.
    i) Are X and Y dependent or independent?

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    This solution provides a detailed, step by step response illustrating how to compute all of the required statistical calculations. The full solution is enclosed in an attached Word document.