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HW5_Problem_Set

# HW5_Problem_Set - ORIE 3500/5500 Fall Term 2008 Assignment...

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Unformatted text preview: ORIE 3500/5500 Fall Term 2008 Assignment 5 Note that • the due date is Monday, October 20 , at 1:00 pm • you need to mention your section number on the top of your answer script. 1. [(3 + 3) + 5 + 4 = 15 pts] On any day of January and February (28 days) the probability that there will be snowfall in Ithaca is 0.4 independently of other days. (a) Suppose there are 4 Sundays and 4 Saturdays in January. If there are exactly 4 days in January with snowfall, what is the con- ditional probability that all of them are (i) Sundays, (ii) either Sunday or Saturday. (b) Find the PMF of total number of days in January and February with snowfall. (c) If you know that there are 40 days of snowfall altogether in Jan- uary and February, then what is the conditional PMF of the num- ber of days with snowfall in February? 2. [3 + 3 + 4 = 10 pts] Let U 1 and U 2 be two independent Uniform (0 , 1) random variables, and V = min { U 1 ,U 2 } and W = max { U 1 ,U 2 } ....
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HW5_Problem_Set - ORIE 3500/5500 Fall Term 2008 Assignment...

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