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2027Hmwk5

# 2027Hmwk5 - ISyE 2027 R D Foley Probability with...

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ISyE 2027 Probability with Applications Fall 2011 R. D. Foley Homework 5 September 26, 2011 due Monday 1. Compute lim n ( 1 - 3 /n ) n - 1 . 2. Certain distributions turn up so often that they have names. So far, we have encountered the Bernoulli, binomial and geometric distributions. For each of the following random variables, if one of the above distribu- tions seems plausible, give the name of that distribution; otherwise, say none of the three. (a) Whether it rains or not tomorrow on campus on January 1st, 2012. (b) The number of days starting from Jan. 1st, 2012 until it rains on campus. (c) The number of days in January 2012 that it rains on campus. (d) Whether the number of days that it rains on cam- pus exceeds 15 or not. (e) The number of days in 2012 until it does not rain on campus. (f) The amount of rain on January 1st, 2012. In doing this problem, let us temporarily assume that whether it rains or not on a particular day is independent of the weather on other days and always has the same probability p . 3. Let X be the roll of a fair die. Let Y = b X/ 3 c where b·c is the “floor function.” (a) What is the p.m.f. of Y ? (b) What is the mean of Y ? (c) What is the second moment of Y ? (d) What is the variance of Y ? (e) What is the standard deviation of Y ? (f) Suppose you could play a game where the payoff is Y

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2027Hmwk5 - ISyE 2027 R D Foley Probability with...

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