# 230hw2 - MATH 230 HOMEWORK 2(Due December 2 2009...

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November 20, 2009 MATH 230 HOMEWORK # 2 (Due: December 2, 2009, Wednesday) [Please, submit your homework to my office (SA 105) by 5:30 PM] (DO NOT forget to write your Section number) 1. To be a winner in the following game, you must be successful in 3 successsive rounds. The game depends on the value of Y , a uniform random variable on (0,1). If Y> 0.1, then you are successful in round 1; if Y >0.2, then you are successful in round 2; and if Y >0.3, you are successful in round 3. a) Find the probability that you are successful in round 1. b) Find the conditional probability that you are successful in round 2, given that you were successful in round 1. c) Find the conditional probability that you are successful in round 3, given that you were successful in round 1 and 2. d) Find the probability that you were a winner. 2. A filling station is supplied with gasoline once a week. If its weekly volume of sales in thousands of gallons is a random variable with probability density function < < - = otherwise x x x f 0 1 0 ) 1 ( 5 ) ( 4

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