Chapter 5: Multiple Random
Variable
Math 217: Probability & Statistics
Marginal PMF
Chapter 5
How to obtain marginal PMF
The definition of marginal PMF show us how to obtain the probability model of X
and the probability model of Y
=
(, )
=
(, )
E

Chapter 5: Multiple Random
Variable
Math 217: Probability & Statistics
Multivariate Joint CDF, PMF & PDF
Chapter 5
Joint CDF, PMF & PDF
Definition: The joint CDF of 1 is
1 1 = [1 1 ]
Definition: The joint PMF of 1 is
1 1 = 1 = 1 =
Definition: The joint

Chapter 5: Multiple Random
Variable
Math 217: Probability & Statistics
Conditional Expected Value
Chapter 5
Discrete case : Definition of E[X] with | (x) replacing ()
Continuous case: Definition of E[X] with | (x) replacing ()
Consider an experiment wi

Recitation 6
Question 1)
Consider the following data set
a) Construct a stem and leaf display for these data.
b) Calculate sample mean, sample standard deviation
c) Construct a histogram for these data.
Solution
a)
b)
Question 2)
The compressive strength

Chapter 6: Statistics
Math 217: Probability & Statistics
Topics
Variance of a Point Estimators
Mean squared error of an estimator
Probability for sampling distribution
Variance of a point estimator
Suppose that 1 and 2 are unbiased estimators.
The va

Chapter 5: Multiple Random
Variable
Math 217: Probability & Statistics
Expected value, Covariance, Correlation
Chapter 5
Expected Value of a Function of Two R.V.
Definition: For random variables X and Y, the expected value of W=g(x,y) is
Discrete: E[W] =

Chapter 4: Continuous Random
Variables
Math 217: Probability & Statistics
Discrete vs Continuous
A discrete random variable is a countable set of numbers
A continuous random variable contains all real numbers between two limits
That means, the probabil

OZYEGIN UNIVERSITY
Spring15, Midterm II April 10th
PROBABILITY AND STATISTICS
MATH 217
(Instructor: Caatay Edemen, Ph.D.)
g
Name: .
ID: .
Q1
Point:
Q2
Q3
Q4
Total
25
25
20
30
100
Score:
Time: 80 Minutes
Permitted Materials: No additional materials are a

OZYEGIN UNIVERSITY
Spring15, Midterm III May 8th
PROBABILITY AND STATISTICS
MATH 217
(Instructor: Caatay Edemen, Ph.D.)
g
Name: .
ID: .
Q1
Point:
Q2
Q3
Q4
Total
30
30
30
30
120
Score:
Time: 80 Minutes
Permitted Materials: No additional materials are all

oZYEéiN UNIVERSITY
Spring"15, Midterm IV~ May 22th
PROBABILITY AND STATISTICS
MATH 217
(Instructor: Qaﬁrttay Edemen, Ph.D.)
Point: 15 15 30 30 30 120
Score:
Time: 80 Minutes
Permitted Materials: No additional materials are allowed
INSTRUCTIONS TO

Chapter 4: Continuous Random
Variables
Math 217: Probability & Statistics
Unit step and impulse function
Chapter 4
How to use these functions
Let Y be a discrete random variable
CDF of Y can be represented by unit step function ()
PMF of Y can be repres

Chapter 4: Continous Random
Variables
Math 217: Probability & Statistics
Erlang Random Variable
Chapter 4
Example-4.11
Gaussian Random Variable
Chapter 4
Gaussian random variable
The graph of has bell shape.
The center of the bell is the parameter , the

Chapter 6: Statistics
Math 217: Probability & Statistics
Topics
Sample Mean
Sample Variance
Sample Standard deviation
Stem-and-leaf diagram
Frequency distribution & histogram
The central limit theorem
Estimating the parameters of a population (the point
e