- 2 Sta2610 013 3 2021 Question 3 45 Marks The Joint Probability Density Function Of Two Continuous Random Variables X A 1 (65.58 KiB) Viewed 41 times
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2 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, fxx (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) (w) P(x<372) (N) P(x < ) (4) (v) E(X). (4) (vi) E(Y). (5) (vii) Marginal probability distribution of X. (5) (viii) Conditional probability distribution of Y given X = 1. (5) (ix) E(Y | X = 1). (5) (x) E(Y < 0.5 | X = 1). (5)