Unformatted text preview: Be sure to explain how you got your answer. 3. (24 pts.) An integer k from 1 to 9 is picked uniformly at random. Let X ( k ) = 1 if k is odd and X ( k ) = 0 if k is even. Let Y ( k ) be the remainder when k is divided by 3. (a) Draw a table like the one here and ﬁll in the probabilities. X \ Y 0 1 2 ? ? ? 1 ? ? ? (b) Compute Cov( X, Y ). 4. (24 pts.) Suppose a strictly decreasing function f : { 1 , 2 } → { 1 , 2 , . . . , n } is chosen uniformly at random. The random variable X is deﬁned by X ( f ) = f (1). (a) Describe choosing f in terms of choosing subsets of a set. (Specify the set, what subsets are chosen, and how they are chosen.) If S is a subset associated with f , what is X in terms of S ? (b) Derive the formula P ( X = k ) = ‰ ( k1) – ( n 2 ) for 1 ≤ k ≤ n , for k < 1 and k > n . END OF EXAM...
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 Fall '01
 Bender
 Math, Probability theory, Numerical digit, digit numbers, ﬁve digit number

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