Suppose that you and your friend go to a concert in Long Beach. You know that I in 200 of the people at the concert will go to UCI (probability of 0.005). You speak to around 50 different people (other than your friend) while you are at the concert. Let X be the number of people you spoke to that also go to UCI. (a) What is the distribution of X? (b) Write the pmf f(x) and describe its parameters. (c) What key assumptions about the people that you spoke to are needed to determine this distribution? (d) What is the expected number of people you speak to that also go to UCI? (e) What is the probability that exactly 3 of the people you speak to go to UCI. Round your answer to 3 sig. fig. (f) What is the probability that you speak to at most 10 people from UCI? (round to 3 decimal places or write an integer as necessary)
Suppose that you and your friend go to a concert in Long Beach. You know that I in 200 of the people at the concert will go to UCI (probability of 0.005). You speak to around 50 different people (other than your friend) while you are at the concert. Let X be the number of people you spoke to that also go to UCI. (a) What is the distribution of X? (b) Write the pmf f(x) and describe its parameters. (c) What key assumptions about the people that you spoke to are needed to determine this distribution? (d) What is the expected number of people you speak to that also go to UCI? (e) What is the probability that exactly 3 of the people you speak to go to UCI. Round your answer to 3 sig. fig. (f) What is the probability that you speak to at most 10 people from UCI? (round to 3 decimal places or write an integer as necessary)
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:2. Suppose that you and your friend go to a concert in Long Beach. You know that 1 in 200 of the people at the concert will go to UCI (probability of 0.005). You speak to around 50 different people (other than your friend) while you are at the concert.
Let \( X \) be the number of people you spoke to that also go to UCI.
(a) What is the distribution of \( X \)?
(b) Write the pmf \( f(x) \) and describe its parameters.
(c) What key assumptions about the people that you spoke to are needed to determine this distribution?
(d) What is the expected number of people you speak to that also go to UCI?
(e) What is the probability that exactly 3 of the people you speak to go to UCI? Round your answer to 3 sig. fig.
(f) What is the probability that you speak to at most 10 people from UCI? (round to 3 decimal places or write an integer as necessary)
Transcribed Image Text:Certainly! Here is the transcribed text suitable for an educational website:
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(g) Now assume that you go to a concert where there are so many people that you will never speak to them all during the time of the concert, so we can think of there being an infinite number of people to speak to (because you won’t run out of people). You keep speaking to new people until you find a fellow Anteater, “Zot Zot”. We can call the number of people that you speak to before you speak to a fellow Anteater Z. What is the distribution of Z?
(h) Using the scenario from part (g), what is the probability that you do NOT speak to anyone from UCI in the first 150 people that you speak to? Round your answer to 3 decimal places.
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