# mid1 - 332:321 Probability and Stochastic Processes October...

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332:321 Probability and Stochastic Processes Examination 1 October 14, 2004 You have 80 minutes to answer the following four questions in the notebooks provided. You are permitted 1 double-sided sheet of notes. Make sure that you have included your name, Rutgers netid and signature in each book used. (5 points) Read each question carefully. All statements must be justified. Computations should be simplified as much as possible. Make sure to read both sides of this exam paper. 1. 30 points SHORT ANSWER You must explain your answer. (a) Events A and B are independent, P [ A ] = P [ B ] and P [ A B ] = P [ A ] + P [ B ]. What is P [ A ]? (b) K is a Poisson = 2 ) random variable. What is P [ K < E [ K ]]? (c) On each turn of the knob, a gumball machine is equally likely to dispense a red, yellow, green or blue gumball, independent from turn to turn. After eight turns, what is the probability P [ R 2 Y 2 G 2 B 2 ] of receiving 2 red, 2 yellow, 2 green and 2 blue gumballs? 2. 50 points A particular birth defect of the heart is very rare; a random newborn infant will have the

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## This note was uploaded on 02/13/2011 for the course 332 226 taught by Professor Staff during the Spring '08 term at Rutgers.

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mid1 - 332:321 Probability and Stochastic Processes October...

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