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University of Toronto Scarborough

Statistics

STAB52H3

Ted Petit

Summer

Description

UTSC Department of Computer and Mathematical Sciences
STA B52 Quiz 11 Version 1
Family Given Student No.
Understanding. Here’s an example of what to expect on a term test or ﬁnal:
A roulette wheel has 18 red wedges, 18 black wedges and 2 green wedges. Wedges are equally likely to come up
in one spin of the wheel. A gambler bets one dollar on red coming up in independent spins of the wheel. Brieﬂy
explain why the gambler shouldn’t play for too long.
Proof.Here’s your quiz question:
Suppose that X ∼ uniform[0,1] and let n = n−1X. Prove that Y n→p X.
n
Problem Solving Theoretical. Here’s an example of what to expect on a term test or ﬁnal:
Suppose that X1,X 2... are independent and uniform on (0,1). LetnM =min {X 1X 2...,X n}.idil n→∞ P(M >n
x/n).
Problem Solving Applied. Here’s an example of what to expect on a term test or ﬁnal:
Suppose that you are trying to collect a complete set of n baseball cards. Suppose you buy them one at a time and
each time you get a randomly chosen card. Let N be the number of cards you have to buy to get the complete
p n
set. Show Nn/(nlnn) −→ 1.
1 UTSC Department of Computer and Mathematical Sciences
STA B52 Quiz 11 Version 2
Family Given Student No.
Understanding. Here’s an example of what to expect on a term test or ﬁnal:
A roulette wheel has 18 red wedges, 18 black wedges and 2 green wedges. Wedges are equally likely to come up
in one spin of the wheel. A gambler bets one dollar on red coming up in independent spins of the wheel. Brieﬂy
explain why the gambler shouldn’t play for too long.
Proof. Here’s your quiz question:
p p
Prove that X n→ 0implies |X n −→ 0.
Problem Solving Theoretical. Here’s an example of what to expect on a term test or ﬁnal:
Suppose that X ,X ,... are independent and uniform on (0,1). Let M =min {X ,X ,...,X }.Fiil P(M >
1 2 n 1 2 n n→∞ n
x/n).
Problem Solving Applied. Here’s an example of what to expect on a term test or ﬁnal:
Suppose that you are trying to collect a complete set of n baseball cards. Suppose you buy them one at a time and
each time you get a rapdomly chosen card. Let N n be the number of cards you have to buy to get the complete
set. Show N n(nlnn) −→ 1.

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