IE265
INTRODUCTION TO PROBABILITY
LECTURE NOTES 10
Department of Industrial Engineering, Middle East Technical University
Banu Lokman
Common Joint Distributions
Multinomial Distribution
The binomial
Fall 2016
IE 265 Introduction to Probability
Study Set 4
Continuous Probability Distributions
1. The time X (in minutes) for a lab assistant to prepare the equipment for a certain lab
experiment is as
Fall 2016
IE 265 Introduction to Probability
Study Set 5
Joint Probability Distributions
1. Two professional wine tasters are asked to rate a sample of wine using a rating scale that
allows them to gi
Fall 2016
IE 265 Introduction to Probability
Study Set 3
1. During a manufacturing process, 15 units are randomly selected each day from the
production line to check the percent defective. From histor
IE265 Introduction to Probability
Fall 2016
Exercises
1. Let X have a uniform distribution on the interval (0,1). Given that X = x, let Y have a uniform
distribution on the interval (0,x+1).
a) Find t
Fall 2016
IE 265 Introduction to Probability
Recitation 4
1. A manufacturer produces 200 ohm resistors. The resistance of a resistor is uniformly
distributed over the interval from 195 ohms to 207 ohm
Fall 2016
IE 265 Introduction to Probability
Recitation 6
1. X and Y are jointly continuous random variables with the following joint probability
density function:
2
35 ( x y ),
f ( x, y )
0,
0 x 3,
Fall 2016
IE 265 Introduction to Probability
Study Set 2
Discrete Random Variables
1. An urn contains 5 red and 5 black chips. You draw 4 chips without replacement. You win
$3 if all 4 are of the same
Fall 2016
IE 265 Introduction to Probability
Study Set 5 KEY
Joint Probability Distributions
1.
a.
x
()
1
0.06
2
0.18
3
0.37
4
0.29
5
0.1
y
()
1
0.06
2
0.18
3
0.37
4
0.29
5
0.1
b. (0.62)
c. ( < 3 |
Fall 2016
IE 265 Introduction to Probability
Study Set 4 KEY
Continuous Probability Distributions
1.
a.
f(x)=1/10
0.12
0.10
0.08
0.06
0.04
0.02
0.00
25
b. (0.2)
c. =30, 2=8.333, =2.887
d. (0.2)
2. (A/
Fall 2016
IE 265 Introduction to Probability
Study Set 3 KEY
1.
a. (0.1710)
b. (0.7168)
2.
a. (0.0052)
b. (0.057)
c. (0.004)
3.
a.
b.
c.
d.
(0.0988)
(0.148)
P(X7)=0.377, E(X)=6
(7.5)
4. (0.8)
5.
a. (0
Fall 2016
IE 265 Introduction to Probability
Recitation 5
1. A coin is tossed twice. Let Z denote the number of heads on the first toss and W the total
number of heads on two tosses. The coin is not f
Fall 2016
January 6, 2017
IE 265 Introduction to Probability
Recitation 7
1. A rectangular shaft with edge length of X2 is going to be assembled into a bearing
with an edge length of X1. Suppose that
IE 252 Network Flows and Integer Programming
Study Set 2
1. Assume that our evacuee is in room 1 (node 1). The safety exit is node 6. The numbers on the arcs
denote the travel times between the subseq
IE 252 Network Flows and Integer Programming
Study Set 3
1. (Delivery Problem) Consider the situation in which orders from m different destinations are delivered
from a central warehouse. Each destina
IE 252 Network Flows and Integer Programming
Study Set 1
1. A Medical Supply Company produces catheters in packs at three production facilities. The company
ships the packs from the production facilit
IE 266 Engineering Statistics
Study Set 3
Spring 2016
The amount of yield Y (ml) obtained in a chemical process is to be related to the
amount of catalyst X (ml) used on a day. The data col
Spring 2016
IE 266 Engineering Statistics
Case Study 3
Due date: May 30, 2016 until 17:30
In answering all questions, please state your assumptions clearly.
After the analysis made for the demand data
IE 266 Engineering Statistics
Study Set 2
The same statistics exam is given three years consecutively and the grades are given in
Grades.xlsx file.
a) Write the hypotheses to test if the grade distrib
Spring 2016
IE 266 Engineering Statistics
Case Study 2
Due date: April 25, 2016 until 17:30
In answering all questions, please state your assumptions clearly.
After the detailed analysis made for dema
Spring 2016
IE 266 Engineering Statistics
Recitation 3
1. The average depth of bedrock at two possible construction sites is to be compared by
driving five piles at random locations within each site.
Spring 2016
IE 266 Engineering Statistics
Case Study 1
Due date: April 4, 2016 until 17:30
In answering all questions, please state your assumptions clearly.
Piece of Cake Bakery whose delicious chees
IE 266 Engineering Statistics
Spring 2016
Introduction
1
What is statistics?
Consumer Price Index increased by 10.06% last year.
In Turkey, one out of 10 people has a criminal record.
2
What is stat
Spring 2016
IE 266 Engineering Statistics
Study Set 1
1. Let be a random variable with mean and variance 2. Two independent random samples
of sizes 1 and 2 are taken. Let 1 and
2 be the corresponding
Spring 2016
IE 266 Engineering Statistics
Recitation 1
1. An experiment is designed to test whether operator A or operator B gets the job of operating
a new machine. Each is timed on 50 independent tr
Spring 2016
IE 266 Engineering Statistics
Recitation 2
1.
A procurement specialist has purchased 31 resistors from Vendor 1 and 25 resistors from
Vendor 2. Each resistors resistance is independent of