ho6 - CS237 Problem Set 6 Random Variables Binomial...

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CS237. Problem Set 6: Random Variables & Binomial Distribution. Graded Problems due Thurs March 3 11:59PM. February 25, 2011 A short problem set for a short week. Reading. Schaum’s Chapter 5.2,5.3,5.10,5.11., and 6.2 L&L Notes on Random Variables. In class we also covered Bloom Filters, M&U 5.5.3. 1 Practice Problems. Exercise 1. Suppose 1 8 of computer programs written by Acme Inc. contain a devastating bug. You purchase 12 random computer programs from Acme. What’s the probability that none of the programs have bugs? That 3 of the programs have bugs? That at least 80% of the programs you bought have bugs? Exercise 2. A ‘sketch’ is a set of n counters ( i.e., a length n vector of integers). You are building up a sketch of stream of packets as follows; for each packet that you see, you draw a random number from 1 , ..., n which tells you which counter in the sketch to increment by one. Consider the i th counter; what is the probability distribution of the value in that counter after you see a total of t packets? Let X be the sum of all
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