Solution
SP 2011
Homework Assignment # 6- Chapter 4
Dr. Goel
Remark: When calculating P(X<A), where X follows a normal distribution with mean=a, std=b,
the formula is P(X<A) = P(X-a)/b<(A-a)/b). Since
Solution
SP 2011
Homework Assignment # 5- Chapter 3 and 4
Dr. Goel
3.68
3.82
3.86:
4.2
d, if k>-5 and k+4<5, i.e, -5<k<1, then
P(k X k 4)
k 4
k
1
dx 0.4
10
If k<-5, then P(k X k 4)
k 4
5
1
k 9
dx
1
Solution
Homework Assignment # 3- Chapter 3
6.
SP 2011
Dr. Goel
Possible X values are 1, 2,(all the positive integers)
Possible samples: S1=(L) each with X=1; S2=(RL,or AL) each with X=2;
S3=(RRL, RAL
STAT 427
Home Work Assignment #2
Dr. Goel
Solution
Spring 2011
REMARK:
In part c, P exactly one P( A1
A2 '
A3 ') P( A1 '
A2
A3 ') P( A1 '
A2 '
A3 )
E. P(M| SS)= P(M and SS)/P(SS)
=(.08+.07+.12)/( .08+
Solution
Homework Assignment # 1
SP 2011
Dr. Goel
A1 cfw_ A2 A3
Note that the above event can also be expressed as
[ A1 cfw_A2 A3 ] [ A2 cfw_A1 A3] [ A3 cfw_A1 A2 ]
Remark for d: you may calculate P
Statistics 427-SP 2011
Midterm II - Solution
Note: Answers to all versions of a question are provided here.
Question 1 (6x2.5 points)
Special Instructions for this question: You DO NOT have to show wo
NAME: Solution to Midterm-1, SP2011
(10 x 4 = 40 points)
Question 1
Special Instructions for this question: You DO NOT have to show work for (a) through (e).
Write the correct choice (A/B/C/D) inside
Joint Distributions -Two or More RVs
Section 5.1
So far we discussed only a single RV
In real (useful) experiments, we usually collect information on two or
more quantities simultaneously
Service Time
Solution
SP 2011
Homework Assignment # 7- Chapter 5
Dr. Goel
1.
a.
P(X = 1, Y = 1) = p(1,1) = .20
b.
P(X 1 and Y 1) = p(0,0) + p(0,1) + p(1,0) + p(1,1) = .42
c.
At least one hose is in use at both isl
Name_
FINAL EXAMINATION - STAT 427
1. [25 points] During slack periods, trucks arrive independently at a weighing station at an
average rate of 10 per hour. Suppose that with probability 0.95 an arriv
zz
by
r a
pYjfbY
u
pgEpYE
y
[email protected]
PA|b
D @ S
AvU
m x a c r c r c x c a Y i q c c g x u u x q Y c Y
6xpyqdFqdEafabYbyYgdaEckdvfdbp&yYwdyddEayqdpjwqdpg n qwdydbn yqfjpd
Y xg u s m igoq q ug q t c cg h
STAT 427: SPRING 2011
INTRODUCTION TO PROBABILITY & STATISTICS I
MWF 10:30- 11:18, 1009 Smith Hall
Instructor:
Prof. Prem K. Goel
E-mail: [email protected]
Office: CH 204C (Cockins Hall) Office Phone: 61
STAT 427
Dr. Goel
Home Work Assignment #7
Sections 5.1, 5.2, 5.4
Spring 2011
10:30-11:18
Due Date: Friday, June 3, 2011
Text Book, Chapter 3-4 Exercises:
Assigned Problems (To be turned in for Credit)
STAT 427
Dr. Goel
Home Work Assignment #6
Sections 4.2-4.4
Spring 2011
10:30-11:18
Due Date: Wednesday, May 25, 2011
Text Book, Chapter 3-4 Exercises:
Assigned Problems (To be turned in for Credit)
4.
STAT 427
Dr. Goel
Home Work Assignment #5
Sections 3.5-4.1
Spring 2011
10:30-11:18
Due Date: Wednesday, May 11, 2011
Text Book, Chapter 3-4 Exercises:
Assigned Problems (To be turned in for Credit)
3.
STAT 427
Dr. Goel
Home Work Assignment #4
Sections 3.3-3.4
Spring 2011
10:30-11:18
Due Date: Wednesday, May 4, 2011
Text Book, Chapter 3 Exercises:
Assigned Problems (To be turned in for Credit)
3.30:
STAT 427
Dr. Goel
Home Work Assignment #3
Sections 3.1-3.3
Spring 2011
10:30-11:18
Due Date: Wednesday April 27, 2011
Text Book, Chapter 3 Exercises:
Assigned Problems (To be turned in for Credit)
3.6
STAT 427
Dr. Goel
Home Work Assignment #2
Sections 2.4-2.5
Spring 2011
10:30-11:18
Due Date: Monday April 18, 2011
Text Book, Chapter 2 Exercises:
Assigned Problems (To be turned in for Credit)
2.45:
STAT 427
Dr. Goel
Home Work Assignment #1
Sections 2.1-2.3
Spring 2011
10:30-11:18
Due Date: Monday April 11, 2011
Assigned Problems (To be turned in for Credit)
Text Book, Chapter 2 Exercises:
2.8: A
Recap .
1. Product Rule for k-tuples
Counts the number of k-tuples you can create when there are n1
choices for the first element, ., nk choices for the kth element:
n1 n2 nk
2. Permutation Rule
Count
5/25/2011
Section 5.4
Distribution of the Sample Mean
Issue: Variability in the Sample Means over repeated sampling
General Result:
Let X1, X2, . , Xn denote a Random Sample from a Large
Population wi
Beyond the Normal Distribution
Section 4.4
Normal Distribution - N(, 2)
Continuous distribution, defined on entire real line (allows positive
density on negative numbers, even though it may be negligi
Statistics 427: Sample Final Exam
Instructions: The following sample exam was given several quarters ago in Stat 427. The
same topics were covered in the class that year. This sample exam is meant to
Final review: Practice problems
1. A manufacturer of airplane parts knows from past experience that the probability is 0.8 that
an order will be ready for shipment on time, and it is 0.72 that an orde
Final review: Practice problems - SOLUTIONS
Note: These are only outlines of the solutions. You have to show all work on the test to get full
credit.
1. P ( delivered on time | ready on time ) = .72/.
Name_
Stat 427
Rumsey, Goel
Midterm 2
Spring, 2006
Remarks:
There are five problems for a total of 100 points.
The number of points for each problem is given in the parenthesis.
You must show full
NAME:_
STAT 427
Prof. Goel
Midterm II
Winter 2002
MWF 11.30-12.30
Important:
This exam is closed book/notes.
You can use a calculator and a single-sided 8.5x11 crib sheet.
You must explain each ste
Review Questions for Midterm 2
Review Set 1
1
2
3
(c)
4
5
6
Review Set 2
7
8
9
10
11
Answer Key
These are just the final answers and not complete solutions. To get full credits,
you will have to show