The distribution function of the mixed random variable Z is given by
Find P(Z = - 2), P(Z = 2), P(- 2< Z< 1), and P(0 ≤ Z ≤ 2).
Answer to relevant QuestionsIf the values of the joint probability distribution of X and Y are as shown in the table Find (a) P(X = 1, Y = 2); (b) P(X = 0, 1 F Y < 3); (c) P(X + Y F 1); (d) P(X > Y). F(x, y) is the value of the joint distribution function of two discrete random variables X and Y at (x, y), show that (a) F(-∞,-∞) = 0; (b) F(q, q) = 1; (c) if a< b and c< d, then F(a, c) ≤ F(b, d). Find the joint probability density of the two random variables X and Y whose joint distribution function is given by Find k if the joint probability density of X, Y, and Z is given by If the joint probability density of X and Y is given by Find (a) The marginal density of X; (b) The marginal density of Y. Also determine whether the two random variables are independent.
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