4 Let X be a rv with pdf f x ax for 0 leq x leq 3 and let Y

4) Let X be a rv with pdf f (x) = ax for 0 leq x leq 3 and let Y be a random variable with pdf f (x) = bx^2 for 0 leq x leq 2 and let Z be a random variable with pdf f(x) = cx^3 for 0 leq x leq 1 a. Determine the appropriate values for a, b, c b. Determine mu x, mu y, mu z c. Determine d. Determine the cdf for each of the random variables. e. Sketch each pdf and cdf 5) You roll two regular/fair six-sided dice. Let X denote the maximum showing on the two dice and let Y denote the sum of the two dice (note that X and Y are random variables). a. Determine the joint density function fx.y(m, n) = P(X = m, Y = n) b. Determine the marginals fx(k) = P(X = k) and fy(k) = P(Y = k) 6) Determine mu z and for Z = X + Y where X is uniform (0, 2) and Y is uniform (0,1). Note. the cdf and pdf for rv Z were established in class.

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