Unformatted text preview: X ∼ N ( μ, σ 2 ) where μ ∼ beta(2 , 2). Compute E [ X ] and var( X ). ◦ 3 (8+8+8+8+8+8=48 points) Suppose ( X, Y ) had the following joint pdf f ( x, y ) = ± cxy, ≤ x ≤ 1 , ≤ y ≤ 1 , else (a) Find c . (b) Compute the marginal distributions for X and Y . (c) Are X and Y independent? (d) Compute cor( X, Y ). (e) Compute the conditional distribution of X  Y . (f) Compute E[ X  Y ]. ◦ 4 (10+10=20 points) Each of ±ve balls are placed in one of four boxes. A ball is placed in box A with probability .1, it is placed in box B with probability .2, it is placed in box C with probability .3, and it is placed in box D with probability .4. Compute the following probabilities. (a) Three balls are placed in box A and two balls are placed in box D. (b) Each box has at least one ball in it....
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 Fall '08
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 Conditional Probability, Probability, Probability theory, Calculation, following joint PDF

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