# stab 52 quiz_1.pdf

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University of Toronto Scarborough

Statistics

STAB52H3

Mike Moras

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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