Question

(c) Let N~DU(100), and let X have the value 10, 20, 25, or 50 with probability 1/4 each, independent of N. If N > X, repeatedly subtract X from N until the result is X or smaller. Let Y be the number left over after this repeated subtraction. The number Y is almost the same as the remainder left over after dividing N into X equal parts, ercept that Y will equal X, not 0, if N is evenly divisible by X. For example, consider the case X-25. If N = 83 then Y 8; if instead N-75 then Y =25; and if i. Write down the conditional distribution of Y given {X , including parameter(s) (2 marks each) ii. Find E (Y|X) (1 mark each) ii. Find E(Y). (1 mark each (2 marks each) iv. Find Cov(X, Y).

Answer 1

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