Course Scores Summary Statistics
STAT 427
Prof. Goel
SPRING 2011
Overall Score: HOMEWORK (60)+ MID-I (80) + MID-II (80) + Final (160) + QA(20)
(Max Score 400)
Summary for Course Score
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STAT 427: SPRING 2011
INTRODUCTION TO PROBABILITY & STATISTICS I
MWF 10:30- 11:18, 1009 Smith Hall
Instructor:
Prof. Prem K. Goel
E-mail: goel.1@osu.edu
Office: CH 204C (Cockins Hall) Office Phone: 614-292-8110
Office Hours: Wed and Fri 11:30 - 12:30
Cour
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)
5.1: A service station has both self-service and full-
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)
4.13: Example 4.5 introduced the concept of time headway
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)
3.68: A certain type of digital camera comes in ( page 12
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: An individual who has automobile insurance (page 106)
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: Starting at a fixed time, each car entering an inters
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: The population of a particular country consists of thre
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: An engineering construction firm is currently working on
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 arriving truck will have
no overweight violations.
a) [5 poi
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 islands.
P(X > 0 and Y > 0) = p(1,1) + p(1,2) + p(2,1)
+ p
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 (X-a)/b follows the standard Normal(0,1),
P(X<A) = P(Z
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
10
10
1
5k
dx
k 10
10
P(k X k 4)
If k>1, then,
5
4.4
(
Solution
SP 2011
Homework Assignment # 4- Chapter 3
Dr. Goel
30.
36.
Let H(X) denote the possible payment by the company, then
EH ( X ) 0 0.8 0.1 (1000 500) 0.08 (5000 500) 0.02 (10000 500) 50 360 190 600
Thus, in order to maintain the expected profit to
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, ARL, AAL) each with X=3 and
S4=(RRAL, RAAL, AARL, RAR
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+0.07+0.12+0.04+0.02+0.05+0.03+0.07+0.08)
=0.27/0.56=0.5
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(at most two errors)=P(no error)+P(1 error)+P(2
errors)
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 work for (a) through (e).
Just fill in the blanks. Any sc
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 the box on the right hand side. Any scratch work will
n
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 Times, # of A/C units
# of cars and # of trucks on a Hwy
fu
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
Counts the number of permutations of size k that can be crea
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 with E[Xi] = and V[Xi] = 2(Called n independent and
ident
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 negligible)
Symmetric
What if we want to model a phenomena tha
The Normal (Gaussian) Distribution
Section 4.3
1. Most used continuous distribution (as probability model) in statistics
Also known as Bell Curve
2. Is used for many physical measurements
heights, weights, test scores (also for errors in measurement)
3.
Recap: Discrete Distributions
r N r
Hypergeometric P( X x) x n x , x maxcfw_0, n ( N r), ,mincfw_n, r
N
n
E( X ) np, where p r / N .
Var( X ) fpc n p 1 p
x 1
xr r
P( X x)
(1 p) p , x = r, r+1,
Negative Binomial
r 1
E( X )
r
p
V (X )
section 3.6
Recap.
Binomial
distribution:
0
x
x
x
x
n
n
n k
p (1 x ) n k
B( x; n, p) p kB(; p) np) ( x; pF (1)p)k b( ;pn, p)
(1 x n, k b nk ( x) n
,p
k 0 k k 0
k 0 k
k 0
k 0 k
x
Hypergeometric Distribution:
1
x 1
x r r
P( X x)
(1 p) p , x = r, r+1,
r 1
r
p
Finite Population of Size N
Each element in the population has a label cfw_0,1 [1 = yes, 0 = no]
Draw a random sample of size n: Two Schemes
Sampling with Replacement
Sampling without Replacement
1
1
5
5
Population:
4
2
4
2
2
3
Sample:
Probability of S
in
Probability Models for Random Variables
Section 3.4
Most of our discussion of probability so far has been related to
an experiment with a finite sample space
(N total outcomes)
where each outcome of the experiment is
equally likely
which lets us compute p
Recap
(Probability) Distribution of X means the specification of:
Probability Mass Function (pmf of X) :
pX(x) = P( X = x) = P ( cfw_ s S : X(s) = x )
Cumulative Distribution Function (cdf of X):
FX(x) = P( X x) = P ( cfw_ s S : X(s) x )
Today .
Some