PS3 Statistics - Third Problem Set PDF

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Third Problem Set...

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Problem Set 3 Statistics Due February 21st, 2019

1. Each day your friend goes to NYU, she has a 20% probability of buying a falafel platter for $6, a 50% probability of buying iced coffee for $3, and a 5% chance of riding a taxi home for $20. Over the course, of a month, she travels to NYU on twenty days. Let F be the amount of money she spends on falafel in a month, C the amount she spends on coffee, and T the amount she spends on taxis. (a) Find E[F ] (b) Find E[T ] (c) Find E[C ] (d) Find E[F + C + T ] 2. You have 100 coins, and 99 of them are fair (equal probability of heads or tails). One of them is weighted and has a 90% probability of landing on heads. You randomly choose one of the 100 coins. Find the probability that it is a weighted coin, under the following scenarios. (a) You flip it 10 times and it lands on heads 9 times (b) You flip it 20 times and it lands on heads 18 times 3. A professor gives students a pop quiz with 5 true or false questions. Eighty percent of the students are well-prepared for the pop quiz, but twenty percent are not. Students who are prepared have a 90% chance of answering each question correctly, but the students who are unprepared simply randomly guess and have a 50% chance. Find the probability that a student was well-prepared under the following scenarios: (a) Answered 3 correctly (b) Answered 4 correctly

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4. A fair coin is flipped 20 times. Your friend proposes a bet where if it lands on heads exactly 10 times, you win $4, but if it lands on heads 11 or more times or 9 or less times, you lose $1. Should you take the bet? In other words, find the expected value of the bet and if it is positive you should take it. 5. Two candidates face each other in an election. The Democratic candidate is supported by 58% of the population, and the Republican candidate is supported by 42%. In other words, if you randomly chose a voter and asked them who they plan to vote for, there would be a 58% chance they would say they support the Democratic candidate. Suppose you run a poll of 8 people (randomly choose 8 people). What is the probability that less than half of them (3 or fewer) would support the Democratic candidate?

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