STAT 400
1.
Spring 2011
Examples for 04/25/2011
A new method of storing snap beans is believed to retain more ascorbic acid than
the old method. In an experiment, snap beans were harvested under uniform
conditions and frozen in 250 equal-size packages. On
STAT 400
Lecture BL1
1.
Practice Problems 10
Fall 2014
Dalpiaz
In a random sample of 100 Hawk & Hummingbird Airline (HHA) direct flights
from New York to Boston, the average number of passengers was 56.3, with
sample standard deviation 11.33.
a)
Construct
Exam 1
1.
Suppose
(Version A white)
P ( A ) = 0.45,
P ( A B ) = 0.15,
P ( B ) = 0.40,
(Answers)
P ( C ) = 0.50,
P ( A C ) = 0.20,
P ( B C ) = 0.25,
P ( A B C ) = 0.05.
a) (2) Find P ( A C ) = _.
b) (3) Find P ( A ( B C ) ) = _.
c) (5) Find P ( B C | A' )
STAT 400
5.
Examples for 02/09/2011
Spring 2011
Management of an airline knows that 0.5% of the airlines passengers lose their
luggage on domestic flights. Management also know that the average value
claimed for a lost piece of luggage on domestic flights
STAT 400
Spring 2011
Examples for 02/11/2011
Binomial Distribution:
1.
The number of trials, n, is fixed.
2.
Each trial has two possible outcomes: success and failure.
3.
The probability of success, p, is the same from trial to trial.
4.
The trials are in
STAT 400
1.
Examples for 02/11/2011
Spring 2011
Binomial, n = 15, p = 1 5 = 0.20.
/
a)
Yes.
b)
E ( X ) = n p = 15 0.20 = 3.
c)
15
P ( X = 3 ) = (0.20 ) 3 (0.80 ) 12 = 0.2501389.
3
OR
P ( X = 3 ) = PMF @ 3 = 0.250.
OR
P ( X = 3 ) = CDF @ 3 CDF @ 2 = 0.648
STAT 400
Spring 2011
Name _
Version B
AD1
AD4
Th 3 4
We 4 5
We 4 5
135 MEB
137 Armory
329 Davenport
165 Noyes
PeiBei Shi
Page
AD3
Th 3 4
Exam 2
AD2
Jong Hyun Yun
Jong Hyun Yun
PeiBei Shi
Please circle your discussion section.
Points
Be sure to show all yo
1.
Award: 10.00 points
ItisSaturdaymorningatStarbucks.Iseachrandomvariablediscrete(D)orcontinuous(C)?
a. Temperatureofthecoffeeservedtoarandomlychosencustomer.
Continuous
b. Numberofcustomerswhoorderonlycoffeewithnofood.
Discrete
c. Waitingtimebeforearand
27.
Award: 10.00 points
The time it takes a ski patroller to respond to an accident call has an exponential distribution with an
averageequalto5minutes.
(a) In what time will 90 percent of all ski accident calls be responded to? (Round your intermediate
c
STAT 400
Spring 2011
Examples for 02/09/2011
5.
Management of an airline knows that 0.5% of the airlines passengers lose their
luggage on domestic flights. Management also know that the average value
claimed for a lost piece of luggage on domestic flights
STAT 400
1.
Outcomes
x
TT
0
HT TH
1
HH
A balanced (fair) coin is tossed twice.
Let X denote the number of H's.
Construct the probability distribution
of X.
2
S = cfw_ HH , HT , TH , TT
X=
Spring 2011
Examples for 02/07/2011 (Answers)
2
1
1
Just for fun:
STAT 400
Spring 2011
Examples for 02/07/2011
A random variable associates a numerical value with each outcome of a
random experiment.
A random variable is said to be discrete if it has either a finite number of
values or infinitely many values that can be
STAT 400
Spring 2011
Name
Version B
ANSWERS
.
AD1
AD3
AD4
Th 3 4
Th 3 4
We 4 5
We 4 5
135 MEB
137 Armory
329 Davenport
165 Noyes
PeiBei Shi
Exam 2
AD2
Jong Hyun Yun
Jong Hyun Yun
PeiBei Shi
Please circle your discussion section.
Page
Points
1
10
partial c
STAT 400
1.
Spring 2011
Examples for 01/26/2011
In Neverland, men constitute 60% of the labor force. The rates of unemployment
are 6.0% and 4.5% among males and females, respectively. A person is selected
at random from Neverlands labor force.
a)
What is
STAT 400
1.
Spring 2011
Examples for 01/26/2011
In Neverland, men constitute 60% of the labor force. The rates of unemployment
are 6.0% and 4.5% among males and females, respectively. A person is selected
at random from Neverlands labor force.
P( U | M )
STAT 400
Examples for 01/28/2011
Spring 2011
Events A and B are independent if and only if
P(BA) = P(B)
P(AB) = P(A)
P(A B) = P(A) P(B)
1.
The probability that a randomly selected student at Anytown College owns a bicycle is
0.55, the probability that a s
STAT 400
Examples for 01/28/2011
Spring 2011
Events A and B are independent if and only if
P(BA) = P(B)
P(AB) = P(A)
P(A B) = P(A) P(B)
Note that if two events, A and B, are mutually exclusive, then P( A B ) = 0. Therefore, two
mutually exclusive events c
STAT 400
Examples for 01/31/2011
Spring 2011
Multiplication Principle ( Fundamental Rule of Counting ):
If there are n events and event i can occur in N i possible ways, then
the number of ways in which the sequence of n events may occur is
N 1 N 2 . N n
STAT 400
Examples for 01/31/2011
Spring 2011
1.
The call letters of radio and television stations in the United States begin with either
K or W. Those west of the Mississippi River start with K and those east of it with W.
a)
Some stations, such as KID in
STAT 400
Spring 2011
Examples for 02/04/2011
order of the selection
is important
order of the selection
is not important
repetitions allowed
(w/ replacement)
nr
n + r 1 Cr
repetitions not allowed
(w/o replacement)
n!
n P r = (n r ) !
n Cr =
n!
r ! (n r )
STAT 400
Spring 2011
Examples for 02/04/2010
order of the selection
is important
order of the selection
is not important
repetitions allowed
(w/ replacement)
nr
n + r 1 Cr
repetitions not allowed
(w/o replacement)
n!
n P r = (n r ) !
n Cr =
n!
r ! (n r )
34.
Award: 10.00 points
Acognitiveretrainingclinicassistsoutpatientvictimsofheadinjury,anoxia,orotherconditionsthatresultin
cognitiveimpairment.Eachincomingpatientisevaluatedtoestablishanappropriatetreatmentprogramand
estimated length of stay. To see if t
STAT 400
Lecture BL1
Fall 2014
Dalpiaz
Homework #5
(due Friday, October 31, by 2:00 p.m.)
Please include your name ( with your last name underlined ), your NetID,
and your discussion section number at the top of the first page.
No credit will be given wit
STAT 400
Lecture BL1
1.
Practice Problems 9
Fall 2014
Dalpiaz
TaxesRUs Block is a national chain that prepares income tax returns for
individuals. The president of the company wants an average number of 5
customers per clerk per day. On April 15, a random
STAT 400
Lecture BL1
1.
Practice Problems 11
Fall 2014
Dalpiaz
Suppose the IQs of students at Anytown State University are normally distributed
with standard deviation 15 and unknown mean.
a)
Suppose a random sample of 64 students is obtained. Find the pr
STAT 400
Practice Problems 12
a)
7.2-2 ( 6.3-2 ) (
b)
1.
)
Use Welchs T to construct a 90% confidence interval for X Y
( without the assumption that the variances are equal ).
2.
7.3-12 (6.5-18 )
(
3.
8.3-14 ( 7.1-20 ) (8.1-20)
4.
8.2-2 ( 7.3-2 ) (
5.
8.2
STAT 400
Lecture BL1
1.
Fall 2014
Dalpiaz
Practice Problems 5
(i) Give the name of the distribution of X (if it has a name), (ii) find the values
of and 2, and (iii) calculate P ( 1 X 2 ) when the moment-generating
function of X is given by
a)
M ( t ) = (
1.1
Properties of Probability
A1 , A2 , ., Ak are mutually exclusive iff Ai Aj = , i 6= j
DeMorgans Laws
1.5
Law of Total Probability and Bayes Theorem
n.b. B is a partition of S.
Bayes Theorem P (Bk |A) =
P (Bk )P (A|Bk )
Pm
P (Bi )P (A|Bi ) k = 1, 2
4.1
Joint Probability Distributions
P
S2 =
ance)
(Xi X)2
n1
(sample vari-
Joint pmf p(x, y) = P (X = x and
Y = y)
X has N (, n ) distribution
Joint
R R pdf P (X, Y ) A) =
f (x, y)dxdy
A
X
/ n
P
P
4.4
Independent Random
Variables
R.V.s X and Y indepen