Suppose X and Y have joint probability distribution fXY
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Suppose X and Y have joint probability distribution fXY

Problem 5

Suppose X and Y have joint probability distribution fXY (x, y) = c(x 2 +xy) on [0, 2]×[0, 2], i.e. 0 ≤ x ≤ 2 and 0 ≤ y ≤ 2.

(a) Find c.

(b) Find the joint cdf FXY (x, y).

(c) Find the marginal cumulative distribution functions FX(x) and FY (y) and the marginal pdf fX(x) and fY (y).

(d) Find E(X) and Var(X).

(e) Find E(Y ) and Var(Y ).

(f) Find the covariance and correlation of X and Y .

Hint
StatisticsProbability distribution is a statistical function which describes all the possible values and the likelihoods which a random variable could take within a range that is given. These distributions come in several shapes with various characteristics, that are defined by the mean, standard deviation, skewness, and also kurtosis. ...

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