CS6313: STATISTICS FOR
DATA SCIENTISTS
Lecture 3: Discrete Random Variables and
Probability Distributions
P(X =0) =
P(X =1) =
P(X =2) =
P(X =3) =
P(X =4) =
0.6561
0.2916
0.0486
0.0036
0.0001
1.0000
DISCRETE RANDOM VARIABLE
PROBABILITY MASS FUNCTION (PMF)
Homework #3. Solution.
IE 230
Textbook: D.C. Montgomery and G.C. Runger, Applied Statistics and Probability for Engineers, John
Wiley & Sons, New York, 2003 (third edition).
Chapter 2, Sections 2.32.7. Chapter 2 is the foundation for the rest of this cour
2-156. The following circuit operates if and only,r if there is a path of functional devices from leﬂ to right. The probability
mat each device Mom is as shown. Assume that the probability that a device is functional does not depend on
whether or not othe
2-156. The following circuit operates if and only,r if there is. a path of ﬁmctional devices from leﬂ to right. The probability
Eli-Lat, each device ﬁmctiona ia as shown. Aaaume that the probability that a device is. functional does not depend on
whether
CS6313: STATISTICS FOR
DATA SCIENTISTS
Lecture 4: Continuous Random Variables and
Probability Distributions
= =0
=
CONTINUOUS RANDOM VARIABLE
() 0
= 1
=
PROBABILITY DENSITY FUNCTION
= =
=
()
CUMULATIVE DISTRIBUTION FUNCTION
+
= =
+
2 =
( )2
7-7. 0 The 'comptessive strength of concrete is normally dis-
tributed with p = 2500 psi and a: 50 psi. Find the probability
that a madam mp1: ofn=5mmaMen
manQiamctcrthatfallsintheimcrval from2499psit025|0psi. 7-36. Suppose that X is the number of observe
CS6313: STATISTICS FOR
DATA SCIENTISTS
Lecture 5: Joint Distributions, Functions of
Random Variables
JOINT PROBABILITY DISTRIBUTION
TABLE
, 0
(, ) = 1
, = ( = , = )
JOINT PROBABILITY MASS FUNCTION
, 0
+
+
, = 1
, =
,
JOINT PROBABILITY DENSITY FUNC
CS6313: STATISTICS FOR
DATA SCIENTISTS
Lecture 1: Introduction
Random Sample: X1, X2, Xn
Population, with some measurable quantity X
Statistic:
1 +2 + +
Random Sample: X1, X2, Xn
Random Sample: X1, X2, Xm
Population 1
Population 2
Statistic-1:
Statistic-2
HOMEWORK 3, STAT 6331
1. Let (X, Y ) denote an iid sample from Geometric(p), that is, the pmf of X is
P (X = k|p) = p(1 p)k1, k = 1, 2, . . .
Consider the statistic T = X Y , and show that it is not sucient.
Hint: It suces to consider a particular value o
SOLUTION FOR HOMEWORK 1, STAT 6331
Welcome to your second homework. Reminder: if you nd a mistake/misprint, do not
e-mail or call me. Write it down on the rst page of your solutions and you may give yourself
a partial credit but keep in mind that the tota
SOLUTION FOR HOMEWORK 1, STAT 6331
Well, welcome to your rst homework. In my solutions you may nd some seeded mistakes
(this is why it is not a good idea just to copy my solution. If you nd them please, do not
e-mail or call me. Instead, write down them o
SOLUTION FOR HOMEWORK 3, STAT 6331
Welcome to your third homework. Reminder: if you nd a mistake/misprint, do not email or call me. Write it down on the rst page of your solutions and you may give yourself
a partial credit but keep in mind that the total
Course Syllabus
Course Information
(course number, course title, term, any specific section title)
STAT 6331.501, STATISTICAL INFERENCE I, FALL 2014
Professor Contact Information
(Professors name, phone number, email, office location, office hours, other
CS6313: STATISTICS FOR
DATA SCIENTISTS
Lecture 2: Basic Probability Concepts
A random experiment is an experiment that can result in different
outcomes, even though it is repeated under the same
conditions. Example: Coin toss, dice roll.
A Sample Space S