CS 70
Discrete Mathematics and Probability Theory
Fall 2017
Kannan Ramchandran and Satish Rao
HW 12 Sundry Before you start your homework, write down your team. Who else did you work with on this homework? List names and email addresses. (In case of homework party, you can also just describe the group.) How did you work on this homework? Working in groups of 3-5 will earn credit for your "Sundry" grade. Please copy the following statement and sign next to it: I certify that all solutions are entirely in my words and that I have not looked at another student’s solutions. I have credited all external sources in this write up. I certify that all solutions are entirely in my words and that I have not looked at another student’s solutions. I have credited all external sources in this write up. (signature here)
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Darts with Friends
Michelle and Alex are playing darts. Being the better player, Michelle’s aim follows a uniform distribution over a circle of radius r around the center. Alex’s aim follows a uniform distribution over a circle of radius 2r around the center. (a) Let the distance of Michelle’s throw be denoted by the random variable X and let the distance of Alex’s throw be denoted by the random variable Y . • What’s the cumulative distribution function of X? • What’s the cumulative distribution function of Y ? • What’s the probability density function of X? • What’s the probability density function of Y ? (b) What’s the probability that Michelle’s throw is closer to the center than Alex’s throw? What’s the probability that Alex’s throw is closer to the center? (c) What’s the cumulative distribution function of U = min{X,Y }? (d) What’s the cumulative distribution function of V = max{X,Y }?
CS 70, Fall 2017, HW 12
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