# hw2 - UCSD ECE 153 Prof Young-Han Kim Handout#7 Thursday...

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UCSD ECE 153 Handout #7 Prof. Young-Han Kim Thursday, October 9, 2008 Homework Set #2 Due: Thursday, October 16, 2008 1. Read Sections 3.1–3.2, 3.4–3.6, 4.1–4.2, 4.4–4.5, 4.7, 4.9, 5.1-5.5, 5.7-5.8 in the text. Try to work on all examples. 2. Juror’s fallacy. Suppose that P ( A | B ) P ( A ) and P ( A | C ) P ( A ). Is it always true that P ( A | B, C ) P ( A ) ? Prove or provide a counterexample. 3. Let X be a geometric random variable with pmf p X ( k ) = p (1 - p ) k - 1 , k = 1 , 2 , . . . . Find and plot the conditional pmf p X ( k | A ) = P { X = k | X A } if: (a) A = { X > m } where m is a positive integer. (b) A = { X < m } . (c) A = { X is an even number } . Comment on the shape of the conditional pmf of part (a). 4. Negative binomial. Suppose we observe an inﬁnite sequence of independent coin ﬂips with bias p (i.e., the probability of heads is p each time). Let X be the number of coin ﬂips until observing k heads. Find the pmf of the random variable

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hw2 - UCSD ECE 153 Prof Young-Han Kim Handout#7 Thursday...

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