Suppose the two-dimensional random variable (X, Y ) is uniformly distributed over the triangle of the figure.
a) What is f.d.p.c. of (X,Y). Calculate P(0 < X ≤ 1, Y > 1). Make a graphic sketch of the region
that you used to calculate the probability.
b) Determine the marginal distributions. (X, Y ) are independent?
c) Find E[X] ,V AR[X], E[Y ] e V AR[Y ];
d) Determine the conditional distributions. Use the conditionals to answer : (X, Y ) are
independent?
e) Calculate E[XY ], γ = Cov(X, Y ) and e ρ = Color(X, Y ). Use the correlation coefficient to
justify the independence between X and Y.
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Suppose the two-dimensional random variable (X, Y ) is uniformly distributed over the triangle of the figure.
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