11/1/2013
5- Joint Probability Distributions
5-1 Two or More Random Variables
5-1.1 Joint Probability Distributions
5-1.2 Marginal Probability
Distributions
5-1.3 Conditional Probability
Distributions
5-1.4 Independence
5-1.5 More Than Two Random
Variable

10/25/2013
3-Discrete Random Variables and
Probability Distributions
3-1 Discrete Random Variables
3-2 Probability Distributions and
Probability Mass Functions
3-3 Cumulative Distribution Functions
3-4 Mean and Variance of a Discrete
Random Variable
3-5 D

10/25/2013
4. Continuous Random Variables and
Probability Distributions
4-1 Continuous Random Variables
4-2 Probability Distributions and
Probability Density Functions
4-3 Cumulative Distribution
Functions
4-4 Mean and Variance of a
Continuous Random Vari

Homework Assignment 1 (Due Date 25 October 2013)
1) Suppose your vehicle is licensed in a state that issues license plates that consist of three digits (between 0
and 9) followed by three letters (between A and Z). If a license number is selected randomly

9/29/2013
CH1: The Role of Statistics in Engineering
CH2: Probability
CH3: Discrete Random Variables and Probability Distributions
CH4: Continuous Random Variables and Prob. Dist.
CH5: Joint Probability Distributions
CH6: Random Sampling and Data Descript

Homework Assignment 2 (Due Date 8 November 2013)
1) An optical inspection system is to distinguish among different part types. The probability of a correct
classification of any part is 0.98. Suppose that three parts are inspected and that the classificat

Homework 4
MAT 281E Linear Algebra and Its Applications
1.
1 3 0 5
A = 2 6 1 16 .
5 15 0 25
Find a basis for each fundamental subspace of A. Determine the dimensions
of these subspaces.
2.
1 0 0
1 3 0 5
A = LU = 2 1 0 0 0 1 6 .
5 0 1
0 0 0 0
Without calcu

Homework 5
MAT 281E Linear Algebra and Its Applications
1. Find the solution of the system of linear equations,
2
5
3
4
0
3
2
2
Ax = b
x1
2
0 0
0 0
x2 = 5
4 0 x3 1
7
x4
1 5
(a) by Cramers method.
(b) by calculating the inverse of A.
2. Given the

HOMEWORK 1
MAT 281E Linear Algebra and Its Applications
1. If kvk = 5 and kwk = 3, what are the smallest and largest values of kv wk?
What are the smallest and largest values of v w? Prove all of your arguments.
2. Consider the equations below.
x+y+z =2
x

Homework 3
MAT 281E Linear Algebra and Its Applications
1. Which of the following are subspaces of R3 ? Prove your arguments.
(a) S = cfw_[b1
b2
b3 ] : b1 = b2
(b) S = cfw_[b1
b2
b3 ] : b1 = 1.
(c) S = cfw_[b1
b2
b3 ] : b1 b2 b3 = 0.
(d) S = cfw_[b1
b2
b

HOMEWORK I
Solutions
1. The length is between 2 and 8. The dot product is between -15 and 15.
2. Yes, it contains the line (Hint: Consider the points satisfying the first two equations). Yes, it has,
e.g. [ 1 1 0], [0 1 1].
3. Use the definition for symme

Homework Assignment 2
MAT 281E Linear Algebra and Its Applications
Yrd. Doc. Dr. Istemihan
Genc
1. By using Gauss elimination method, determine if
a solution exists for each linear system of equations below and find the solutions if there exists
any.
(a)

Homework III
Solutions
1. (a) subspace (b) not a subspace (c) not a subspace (d) subspace (e) not a subspace
(f) subspace.
2. See lecture notes
3. = is solvable if and only if + 2 = 0.
2 4
= 2 , 5.
2 3
= is solvable if and only if ().