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pre you find soneone who voted John Smith: :) = P(polled k persons before find someone voted for John) = ( out computing any individual probability associated to cach vali om variable X could take on, show that the function above fulfl y conditions in order to be defined as a probability mass functio 2 0 and EoP(k) = 1). ose 0.3. Using the cdf, what is the probability that at lea sons did not vote John Smith? Write the proper notation for d ability. Keep 3 decimal places. e number of minutes someone spends inside the Birdcoop gym is ally with mean 30 minutes - that is, follows a Erponential() d at each person's time spent at the gym is independent from each

pre you find soneone who voted John Smith: :) = P(polled k persons before find someone voted for John) = ( out computing any individual probability associated to cach vali om variable X could take on, show that the function above fulfl y conditions in order to be defined as a probability mass functio 2 0 and EoP(k) = 1). ose 0.3. Using the cdf, what is the probability that at lea sons did not vote John Smith? Write the proper notation for d ability. Keep 3 decimal places. e number of minutes someone spends inside the Birdcoop gym is ally with mean 30 minutes - that is, follows a Erponential() d at each person's time spent at the gym is independent from each

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 10CYU
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Question 3 (a) Suppose you are outside a polling station during a local election and asking people if they voted for a specific independent candidate, John Smith. Consider the answer you get from each person follows a Bernoulli distribution with success rate TE (0,1), where success represents the event that a person voted for John Smith. Then, the geometric distribution would represent the variable X, which is the number of people you had to poll before you find someone who voted John Smith: p(X = k) = P(polled k persons before find someone voted for John) = (1-7)*7, Vk €N. i) Without computing any individual probability associated to each value that the random variable X could take on, show that the function above fulfills the nec- essary conditions in order to be defined as a probability mass function pmf (i.e. p(k) > 0 and P(k) = 1). ii) Suppose T = 0.3. Using the edf, what is the probability that at least the first 3 persons did not vote John Smith? Write the proper notation for defining the probability. Keep 3 decimal places. (b) Suppose the number of minutes someone spends inside the Birdcoop gym is distributed Exponentially with mean 30 minutes - that is, follows a Erponential() distribution. Assume that each person's time spent at the gym is independent from each other. Note that if X ~ Exponential(A) then the CDF is given by P(X <r) = 1- e a i) What is the probability that someone will spend more than 60 minutes at the gym? Round to 3 decimal places. ii) Suppose X1,..., X, are independently and identically distributed Erponential(X). Let S, = min(X1,..., X,). Show that the CDF of S, is 1-e Aa. Azn iii) Suppose the Birdeoop gym is at capacity, at 60 people. Assume everyone who is currently in the gym began their workout at the same time. You are next in line to get into the gym. What is the probability yon will wait less than 1 minute to get in? Use the same ) * as in part a). Round your answer to 3 decimal %3D places.
Transcribed Image Text:Question 3 (a) Suppose you are outside a polling station during a local election and asking people if they voted for a specific independent candidate, John Smith. Consider the answer you get from each person follows a Bernoulli distribution with success rate TE (0,1), where success represents the event that a person voted for John Smith. Then, the geometric distribution would represent the variable X, which is the number of people you had to poll before you find someone who voted John Smith: p(X = k) = P(polled k persons before find someone voted for John) = (1-7)*7, Vk €N. i) Without computing any individual probability associated to each value that the random variable X could take on, show that the function above fulfills the nec- essary conditions in order to be defined as a probability mass function pmf (i.e. p(k) > 0 and P(k) = 1). ii) Suppose T = 0.3. Using the edf, what is the probability that at least the first 3 persons did not vote John Smith? Write the proper notation for defining the probability. Keep 3 decimal places. (b) Suppose the number of minutes someone spends inside the Birdcoop gym is distributed Exponentially with mean 30 minutes - that is, follows a Erponential() distribution. Assume that each person's time spent at the gym is independent from each other. Note that if X ~ Exponential(A) then the CDF is given by P(X <r) = 1- e a i) What is the probability that someone will spend more than 60 minutes at the gym? Round to 3 decimal places. ii) Suppose X1,..., X, are independently and identically distributed Erponential(X). Let S, = min(X1,..., X,). Show that the CDF of S, is 1-e Aa. Azn iii) Suppose the Birdeoop gym is at capacity, at 60 people. Assume everyone who is currently in the gym began their workout at the same time. You are next in line to get into the gym. What is the probability yon will wait less than 1 minute to get in? Use the same ) * as in part a). Round your answer to 3 decimal %3D places.
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