Question

Pink Panther Question

D. Each day (independently of all other days) Jill has a 1/5000 chance of hearing a particular fact: let's say the fact that Henry Mancini composed "The Pink Panther Theme." Jill stores something in long term memory after hearing it 3 times. Use Poisson approximations to (approximately) answer the following (a) What is the probability that, by the time Jill is 10,000 days old, she knows that Henry Mancini wrote "The Pink Panther Theme"? Alice reads more than Jill and has a better memory for trivia. Each day (independently of all others) Alice has a 1/1000 chance of learning that Henry Mancini wrote "The Pink Panther Theme," and she stores information in long term memory after hearing it twice (b) What is the probability that, by the time Alice is 10,000 days old, she knows that Henry Mancini wrote "The Pink Panther Theme"? (c) If there are 10, 000 similar facts (each fact comes with same probabilities as above), how many of them do we expect that Jill knows but Alice doesn't (assuming that both are 10,000 days old)? Assume that for each given fact, the two Poisson random variables (number of times fact is heard by Alice and by Jill) are independent. (If the answer is small, then Jill should feel pretty lucky when one of these facts comes up while she is watching Jeopardy with Alice.)

Answer 1

Date Pace ibutar whare ns no.of smples For Poisson's distr p polit S000 2 -2 e. -O135-021-0.21 ,323 LOoO af hearinat least toise 0.995

2. 0.323x 0.000s