Probability and Stats for Engineers FULL YEAR COURSE
MATHEMATIC MATH2377Y

Fall 2012
MAT2377
Assignment 4
Solutions
Due date: 12 November 2012
Total number of points: 20 plus bonus question
Q1. Time to reaction to a visual signal follows normal distribution with mean 0.5 seconds and standard deviation
0.035 seconds.
(a)
What is the probab
Probability and Stats for Engineers FULL YEAR COURSE
MATHEMATIC MATH2377Y

Fall 2012
MAT2377  Assignment 1
Total number of points: 33
Important:
The assignments have to be handed in the lobby of the Department of Mathematics and Statistics (in
the box marked MAT 2377) on the due date, no later than 14:30. Late assignments cannot be acce
Probability and Stats for Engineers FULL YEAR COURSE
MATHEMATIC MATH2377Y

Fall 2012
Assignment 3
Total number of points: 13
Q1. Suppose that the random variable X has the following cumulative distribution function CDF:
x0
0,
FX (x) =
x3 , 0 x 1
1,
x 1.
(a)
Compute P (X > 0.5) and P (0.2 < X < 0.8).
(b)
Find the probability density funct
Probability and Stats for Engineers FULL YEAR COURSE
MATHEMATIC MATH2377Y

Fall 2012
Assignment 6
Due date: 6 December 2012
Q1. Ten individuals have participated in a diet modication program to stimulate weight loss. Their weight both
before and after participation in the program is shown below:
Before
After
195, 213, 247, 201, 187, 210,
Probability and Stats for Engineers FULL YEAR COURSE
MATHEMATIC MATH2377Y

Fall 2012
MAT2377 (Fall 2012)  Assignment 2
Total number of points: 28
Important:
The assignments have to be handed in the lobby of the Department of Mathematics and Statistics (in
the box marked MAT 2377) on the due date, no later than 14:30. Late assignments ca
Probability and Stats for Engineers FULL YEAR COURSE
MATHEMATIC MATH2377Y

Fall 2012
Assignment 5
Solutions
Total number of points: 25
Q1. Past experience indicates that the breaking strength of yarn used in manufacturing drapery material is normally
distributed and that = 2 psi. A random sample of 15 specimens is tested and the average b
Probability and Stats for Engineers FULL YEAR COURSE
MATHEMATIC MATH2377Y

Fall 2012
MAT2377  List of topics for nal exam
Compute probabilities and conditional probabilities using a table;
Compute probabilities (using the addition rule, independence etc.):
Conditional probability, total probability rule and Bayes Theorem:
Probability
Probability and Stats for Engineers FULL YEAR COURSE
MATHEMATIC MATH2377Y

Fall 2012
Multiple choice set 2
This set of questions covers material from Section 3. Multiple choice is the same format as for the midterm.
Full solutions to be posted later.
Q1. Twelve items are independently sampled from a production line. If the probability any
Probability and Stats for Engineers FULL YEAR COURSE
MATHEMATIC MATH2377Y

Fall 2012
Multiple choice set 5
n
For Questions 812 assume that n = 25,
n
i=1
n
x2 ,
i
xi ,
i=1
n
i=1
n
2
yi and
yi ,
i=1
xi yi are, respectively,
i=1
325.0000, 5525.0000, 658.9717, 22631.3766, 11153.5882.
Note that t0.05/2,23 = 2.069.
Q1. A new cure has been deve
Probability and Stats for Engineers FULL YEAR COURSE
MATHEMATIC MATH2377Y

Fall 2012
Multiple choice set 3
This set of questions covers material from Section 4. Multiple choice is the same format as for the midterm.
Full solutions to be posted later.
Q1. Consider a random variable X with the following p.d.f:
if x 1
0
3
2
f (x) =
(1 x ) i
Probability and Stats for Engineers FULL YEAR COURSE
MATHEMATIC MATH2377Y

Fall 2012
Multiple choice set 1
This set of questions covers material from Section 2. Multiple choice is the same format as for the midterm.
Q1. Two events each have probability 0.2 of occurring and are independent. The probability that neither occur is
(a)
0.64
(b
Probability and Stats for Engineers FULL YEAR COURSE
MATHEMATIC MATH2377Y

Fall 2012
Multiple choice set 4
Q1. If X N (0, 4) the value of P(X 2.2) is (use the norma table)
(a)
0.232131
(b)
0.843822
(c)
0.252689
(d)
0.2713
(e)
0.728622
Solution to Q1:
P (X 2.2) =
1 P (X 2.2) = 1 P (2.2 X 2.2) =
X 0
2.2 0
2.2 0
= 1P
=
4
4
4
= 1 (1