ENME392 Spring 2016 Written homework 1 Due in class Tuesday 2/23 as hardcopy 1. A type of radio transmits data across the Atlantic Ocean. The number of errors in the transmission during any given amount of time approximately follows a Poisson distribution. The mean number of errors is 2 per hour. (a) What is the probability of having at least 3 errors during a 90-minute period? (b) What is the median length of time between errors? 2. A computer uses passwords that consist of the 26 letters (a-z) and the 10 numbers (0-9). How many dierent passwords are possible if: (a) Exactly 6 characters (letters or numbers) are required, and the letters are not case-sensitive (i.e., no dierence between upper- and lower-case)? (b) Passwords must have 4 letters followed by 2 numbers, again without being case-sensitive? (c) Passwords have 4-6 characters, and they are case-sensitive? (d) Passwords have 6 characters, not case-sensitive, but no character can appear more than once? (e) A student wrote their password on a piece of paper, cut out each letter (all lowercase a-z), mixed them, and placed them in front of you. There are 6 pieces. How many possible passwords could the student have? 3. The UMD health clinic noticed a spike in visits by students with u-symptoms. They had 100 students visit in total. Of these, 10 had the normal u, 40 had a type of stomach u, and 50 were completely healthy. They asked each student whether they had eaten at the Swedish restaurant on campus. Overall, 30 students had eaten there, and 13 of those had gotten the stomach u while 2 of those had gotten the normal u. (a) How many students had both the stomach and the normal u? (b) What is the probability of having either type of u if you had eaten at that restaurant? (c) Did going to that restaurant change the risk of contracting dierent us, i.e., are the events of visiting the restaurant and contracting dierent us independent? 4. In Olympic speed-skating, 2 Americans called Bob and Joe are competing. Their results are normally distributed, with means of 120 and 121 seconds and standard deviations of 3 and 5 seconds, respectively. The fastest non-American skater (i.e., among everyone except Bob and Joe) records a time of 118 seconds (the fastest time wins, of course). (a) Sketch the distribution of Bobs results, and show graphically (with numbers added) how likely he is to nish at least second? (b) How likely is it that an American wins the gold medal? (c) How likely is it that Americans win both the gold and the silver? 5. An exclusive club for top students has to elect a new President and Treasurer. There are 50 students in the club, and all are eligible for election. No person can have two jobs. How many dierent choices of ocers are possible if: (a) There are no restrictions? (b) One person will serve only if he/she is President? (c) Two people will serve together or not at all? ENME392 Spring 2016, University of Maryland 1