Family name, comma, personal name:_ Your student ID:_
UNIVERSITY OF TORONTO Faculty of Arts and Science ACT245H1S Winter 2007 Duration 2 Hours Aids: All calculators allowed. Scrap paper OK.
Instructor: Keith Sharp PhD FSA
NOTES: 1. Scrap is to be handed i
Name:
Student #:
Quiz 1: Math Review
Duration: 50 min
Total: 5 Marks
1
1. (0.5) Find lim (1 + x )x
x
2. (0.5) Find lim
x0
3. (0.5)
sin x
x
d x ln x
dx ex
1
x5 ex dx
4. (0.5) Find
0
5. (1) For what value(s) of n such that
1
6. (1)
0
1
dx
xn
1 x
e dx
2
<
7.
Name:
Student #:
Quiz 4
Duration: 1 Hour
Total: 10 Marks
1. An insurance company sells an auto insurance policy that covers losses incurred by a policyholder, subject to a deductible of $100. Losses incurred follow a gamma distribution with
mean 300 and s
Name:
Student #:
Quiz 2
Duration: 50 min
Total: 10 Marks
1. (1 Mark) A survey of an insurance companys medical policyholders in the last three years
revealed the following information:
31% made claims for dental care
27% made claims for optical care
21
ACT245H1S
PROBLEM SET 2
1. The area of the shaded region is:
B) b
A)
C)
b
D) b
E)
2. Find the area of the intersection of the two circles % b & ~ , and ~
A) b
l
B) b
l
C) b
l
l
D) c
E) c
l
l%
3. Let be a continuous function on l and let 0 ~
cl% % &
NAME:
STUDENT NO:
(Last Name, First Name)
University of Toronto at Mississauga
act245h5s Test 1, February 13, 2006
Duration: 60 min
Instructions:
You are allowed to use at most two nonprogrammable calculators.
Do not spend too much time on one question,
ACT245H1 S - PROBLEM SET 6
1. Let ? be a discrete random variable with probability function
7 ? ~ % ~ % for % ~ What is the probability that ? is even?
A)
B)
C)
D)
E)
2. For a certain discrete random variable on the non-negative integers, the probabi
ACT245H1S
1. For what values of % is O% b %O ?
A) c %
B) % c or %
PROBLEM SET 1
C) % c
D) %
E) %
2. If % b %& b & ~ and % b l%& b & ~ then % b & ~ ?
A)
l
b
B)
C)
lbl
D)
E)
3. Transform to rectangular coordinates: c ~ l .
A) % b & ~ c l
Name:
Student #:
Quiz 3
Duration: 50 min
Total: 10 Marks
1. A random variable X has the cumulative distribution function:
0
for x < 1
x2 2x+2
F (x) =
for 1 x < 2
2
1
for x 2
Find the variance of X.
(a)
(b)
(c)
(d)
(e)
1
8
4
3
23
12
7
72
5
36
1
2. An insu
ACT245H1 S - PROBLEM SET 7
1. ? has a discrete uniform distribution on the integers and @ has a
discrete uniform distribution on the integers . Find = ? c = @ .
A) b
B)
C)
D) c
E) c b
2. The probability that a particular machine breaks down in any day
ACT245H1 S - PROBLEM SET 5
1. A class contains 8 boys and 7 girls. The teacher selects 3 of the children at random and
without replacement. Calculate the probability that number of boys selected exceeds the
number of girls selected.
A)
B)
B)
B)
B
ACT245H1S
PROBLEM SET 3
1.
1B % 1 1 % ~
b
A) (1 b c1 ) B) c (1 b c1 )
E) Does not exist
C) (1 b )
D) !(12 )
B
2. Let (%) ~ % (1 c % ) for O%O 1. Determine the value of % such that (%) ~ c 2 .
3
~0
A) c 1
2
3.
B) c 1
3
C) 1
9
E) 1
2
E) 3
B
~1
B
~0
(% c 1)
Family name, comma, personal names:_
Your student ID:_
Your signature: _
UNIVERSITY OF TORONTO
Faculty of Arts and Science
ACT245 Sum09
TERM TEST 1, JULY 8, 2009
Duration 50 Minutes
Aids: All calculators allowed. Scrap paper OK if needed.
Instructor: Keit
Family name, comma, personal names:_
Your student ID:_
Your signature: _
UNIVERSITY OF TORONTO
ACT245 W2011
TERM TEST 1
Duration 50 Minutes
Aids: All non-programmable calculators allowed. Scrap paper OK if needed.
Instructor: Keith Sharp PhD FSA FCIA CFA
NAME:
STUDENT NO:
(Last Name, First Name)
University of Toronto at Mississauga
act245h5s Test 2, March 27, 2006
Duration: 60 min
Instructions:
You are allowed to use at most two nonprogrammable calculators.
Do not spend too much time on one question, an