MAT 2371
Fall 2016
Solution to assignment 1
1.i: Using the multiplication principle the sample space
S = cfw_(x1 , . . . , xn ) : xi = 1, 2, 3, 4
has
4 4 . . . 4 = 4n
possible outcomes.
1.ii: To fill the n coordinate (x1 , . . . , xn ), we need to choose

MAT 2371
Fall 2016
Assignment 5
Due on Tuesday, December 6, 2016 in class.
[10]1. 10 independent observations are chosen at random from an exponential
distribution with mean 1.
Calculate the probability that at least 5 of them are in the interval (1, 3).

MAT 2371
Fall 2016
Assignment 4
Due on Thursday, November 24, 2016 in class.
[21]1. Let X be a random variable with exponential distribution with mean 1.
(i) Write the p.d.f. for the random variable X.
exp(x), if 0 < x
f (x) =
0
if Otherwise
(ii)
R
exp(x)

MAT 2371
Fall 2016
Assignment 3
Due on Tuesday, November 1, 2016 in class.
[17]1. Let X be a random variable with the probability mass function
x
2
, x = 1, 2, 3, . . .
f (x) = c
3
and zero, otherwise. Find
(i) Calculate c.
(i) We know
X
f (x) = 1 = c
x

MAT 2371 (Fall 2016)
Introduction to Probabaility
Professor :
M. Zarepour
Email : zarepour@uottawa.ca
Bureau : 585 King Edward (KED), Room 207D
Telephone : 562-5800 ext. 3503
Web : http:/aix1.uottawa.ca/~zarepour/
Course Schedule:
Tuesday 10:00 - 11:30 TB

MAT 2371, Final Exam Formula Sheet
1
MAT 2377 (Fall 2016)
Final Exam Formula Sheet
Addition Rule: P (A B) = P (A) + P (B) P (A B)
Conditional probability of A given B:
P (A|B) =
P (A B)
P (B)
Total probability rule:
P (A) = P (A B) + P (A B 0 ) = P (A|

MAT 2371
Fall 2016
Assignment 1
Due on Tuesday, October 18, 2016 in class
20 points for each question.
1. Let A and B be two events such that P (A) = 2/5 and P (B) = 7/10.
(i) Calculate P (A B).
(ii) If A and B are mutually exclusive find P (B|A) and P (A

MAT 2371 Fall 2016
Solution to Assignment 2
Professor: M. Zarepour
Question 1.
(i) We have
P (A B) = P (A) + P (B) P (A B) = P (A) + P (B) P (A)P (B) = 0.4 + 0.7 0.4 0.7 = 0.82
(ii) From the definition we get
P (B|A) = P (B A)/P (A) = 0.
Similarly
P (A|B)

MAT 2371
Fall 2016
Assignment 3
Due on Tuesday, November 1, 2016 in class.
[17]1. Let X be a random variable with the probability mass function
x
2
, x = 1, 2, 3, . . .
f (x) = c
3
and zero, otherwise. Find
(i) Calculate c.
(ii) P (X > 4|X > 2).
(iii) P

MAT 2371
Fall 2016
Assignment 1
Due on Tuesday, September 27, 2016 in class
1. (21 Points) A 4-sided is rolled n times
(i) How many possible outcomes do we have?
(ii) For 0 i n, in how many possible outcomes the side 1 appear i times?
(iii) Prove
n
4 =
n

MAT 2371
Fall 2016
Assignment 3
Due on Tuesday, November 1, 2016 in class.
[17]1. Let X be a random variable with the probability mass function
x
2
, x = 1, 2, 3, . . .
f (x) = c
3
and zero, otherwise. Find
(i) Calculate c.
(i) We know
X
f (x) = 1 = c
x