MATH2404 - Introduction to Probability Theory
Exercise Set 4
June 11, 2014
1. (a) Serious delays on Mona Road occur at random, at an average rate of one per week. Show
that the probability of at least 4 serious delays occurring during a particular 4-week
MATH2404 - Probability Theory
Problem Paper 2
Due Date: September 25, 2014
1. A factory has three machines A, B and C that make 20%, 30%, and 50% of the total production, respectively. Of their output, machine A produces 3% defective items, while machine
MATH2404 - Probability Theory
Problem Paper 1. Due September 11, 2014
1. Two fair cubical dice are thrown. Find the probability that:
(a) the sum of the scores is 11;
(b) the sum of the scores is 5;
(c) none of the dice show a 3;
(d) the product of the sc
MATH2404 - Introduction to Probability Theory
Exercise Set 5
June 13, 2014
1. An unbiased cubical die has the number 1 on one face, the number 2 on two faces and the
number 3 on three faces. The die is rolled twice and X is the total score.
(a) Find the p
MATH2404 - Introduction to Probability Theory
Exercise Set 3
June 09, 2014
1
2
1
1. Two events A and B are such that P(A) = , P(A|B) = and P(B|A) = .
4
2
3
(i) Are A and B independent events?
(ii) Are A and B mutually exclusive events?
(iii) Find P(A B).
MATH2404 - Probability Theory
Exercise Set 1
June 02, 2014
1. (a) In how many ways can the letters the word M AT HEM AT ICS be arranged?
(b) If the letter of the word M AT HEM AT ICS are arranged in a line at random, what is
the probability that the arran
MATH2404 - Introduction to Probability Theory
Exercise Set 6
June 16, 2014
1. The continuous random variable X has probability density function given by
k
,
for x 0,
f (x) =
(x + 1)4
0,
for x < 0,
where k is a constant.
(a) Show that k = 3, and find the
MATH2404 - Introduction to Probability Theory
Problem Paper 4
Due Date: October 14, 2014
1. The random variable X has an exponential distribution with parameter .
(a) Find the second E(X 2 ) and the third E(X 3 ) moments of X;
(b) For = 2 find the probabi
MATH2404 - Probability Theory
Problem Paper 3
Due Date: September 30, 2014
1. A quality control inspector takes a sample of 10 toy trucks at random from a production line.
10% of the trucks coming off the line have missing wheels. Calculate the
(a) expect
MATH2404 - Introduction to Probability Theory
Exercise Set 2
June 06, 2014
1
4
1
1. Events A and B are such that P(A) = , P(B|A) = , and P(B 0 |A0 ) = . By drawing a tree
3
4
5
diagram or otherwise, find
(a) P(B 0 |A)
(b) P(A B)
(c) P(B)
(d) P(A B)
2. In
MATH2404 - Introduction to Probability Theory
Problem Paper 5
Due: November 4, 2014
1. The heights of university students at the Faculty of Pure and Applied Sciences are Normally
distributed with mean 1.5m and variance 0.3m. If a student is chosen at rand