STA2610/013/3/2021 Question 3 [45 Marks] The joint probability density function of two continuous random variables X and

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Sta2610 013 3 2021 Question 3 45 Marks The Joint Probability Density Function Of Two Continuous Random Variables X And 1 (89.93 KiB) Viewed 45 times

STA2610/013/3/2021 Question 3 [45 Marks] The joint probability density function of two continuous random variables X and Y is uniform over the region 0 < x < 4,0 < y and x-1 < y < x + 1. That is, fxy (x, y) = c for x and y in the region. (3) (i) The graph of the range of (X, Y). Determine the following: (ii) The value for c such that fxy(x, y) is a joint probability density function. (5) (4) (H) P(x <3,8<) iv) P(x < ) (4) (v) E(X). (4) (5) (5) (vi) E(Y). (vii) Marginal probability distribution of X. (viii) Conditional probability distribution of Y given X = 1. (ix) E(Y | X = 1). (x) E(Y < 0.5X = 1). (5) (5) (5) Question 4 [10 Marks] Let Y be a random variable with a density function given by f(y) = y, 1, 0, 0 < y1 1<ys i elsewhere. Find the probability density function for U if U = 10Y - 4. (10) Total: [100] 3