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# stab 52 quiz_1.pdf

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School
University of Toronto Scarborough
Department
Statistics
Course
STAB52H3
Professor
Mike Moras
Semester
Fall

Description
UTSC Department of Computer and Mathematical Sciences STA B52 Quiz 1 Version 1 Family Given Student No. Understanding. Here’s an example of what to expect on a term test or ▯nal: The probability of winning the jackpot when playing one ticket of lotto 649 is approximately 1/14000000. What does this mean empirically? Proof. Here’s an example of what to expect on a term test or ▯nal: Suppose P([0;1)) = 1. Prove that there is some n such that P([0;n]) > 0:9. Problem Solving Theoretical.Here’s your quiz question: Suppose we choose a positive integer at random, according to some unknown probability distribution. Suppose that we know that P(f1;2;3;4;5g) = 0:3, that P(f4;5;6g) = 0:4 and that P(f1g) = 0:1. What are the largest and smallest possible values of P(f2g)? Problem Solving Applied. Here’s an example of what to expect on a term test or ▯nal: Suppose that in a network of 3 computers, at a given time the event that the kth computer is down has (un- conditional) probability p for k = 1;2;3: Moreover, there is probability p of power failure, in which case all the k computers are down, but given that there is no power failure the computers are up or down independently of each other. Calculate the probability that at this time there is at least one computer up. 1 UTSC Department of Computer and Mathematical Sciences STA B52 Quiz 1 Version 2 Family Given Student No. Understanding. Here’s an example of what to expect on a term test or ▯nal: The probability of winning the jackpot when playing one ticket of lotto 649 is approximately 1/14000000. What does this mean empirically? Proof. Here’s an example of what to expect on a term test or ▯nal: Suppose P([0;1)) = 1. Prove that there is some n such that P([0;n]) > 0:9. Problem Solving TheoreticalHere’s your quiz question: Let P be some probability measure on the sample space S = [0;1]: Show by example that we might have lim P([0;1=n)) > 0: n!1 Problem Solving Applied. Here’s an example of what to expect on a term test or ▯nal: Suppose that in a network of 3 computers, at a given time the event that the kth computer is down has (un- conditional) probabilitk p for k = 1;2;3: Moreover, there is probability p of power failure, in which case all the computers are down, but given that there is no power failure the computers are up or down independently of each other. Calculate the probability that at this time there is at least one computer up. 2 UTSC Department of Computer and Mathemat
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