STAT 408
Spring 2014
Practice Problems 2
1.
Every day, Marge remembers to feed Santa's Little Helper (the name of the dog)
with probability 0.60. Homer remembers to feed the dog with probability 0.30.
Find the probability that either Marge or Homer (or bo
STAT 408
Spring 2012
Name _
Version A
Exam 2
Page
Be sure to show all your work; your
partial credit might depend on it.
Earned
1
Put your final answers at the end of
your work, and mark them clearly.
2
If the answer is a function,
its support must be inc
Practice Problems 5
1.
The heights of adult males in Neverland are normally distributed with mean of
69 inches and standard deviation of 5 inches.
a)
What proportion of adult males in Neverland are taller than 6 feet (72 inches) ?
b)
What proportion of ad
Practice Problems 3
1.
During a radio trivia contest, the radio station receives phone calls according to Poisson
process with the average rate of five calls per minute. Find the probability that the ninth
phone call would arrive during the third minute.
STAT 408
Spring 2012
Homework #4
(due Friday, February 17, by 3:00 p.m.)
Be sure to show all your work; your partial credit might depend on it.
No credit will be given without supporting work.
1.
Sally sells seashells by the seashore. The daily sales X of
STAT 408
Spring 2012
Homework #10
(due Friday, April 6, by 3:00 p.m.)
1.
Let X and Y have the joint p.d.f.
f X Y ( x , y ) = 20 x 2 y 3 ,
0 < x < 1, 0 < y <
x,
zero elsewhere.
a)
Find f X | Y ( x | y ).
b)
Find E ( X | Y = y ).
c)
Find f Y | X ( y | x ).
STAT 408
Spring 2012
Homework #4
(due Friday, February 17, by 3:00 p.m.)
Be sure to show all your work; your partial credit might depend on it.
No credit will be given without supporting work.
1.
Sally sells seashells by the seashore. The daily sales X of
STAT 408
Spring 2012
Homework #2
(10 points)
(due Friday, February 3, by 3:00 p.m.)
1.
A bank classifies borrowers as "high risk" or "low risk," and 16% of its loans are
made to those in the "high risk" category. Of all the bank's loans, 5% are in default
STAT 408
Spring 2012
Homework #10
(due Friday, April 6, by 3:00 p.m.)
1.
Let X and Y have the joint p.d.f.
f X Y ( x , y ) = 20 x 2 y 3 ,
a)
f Y( y ) =
f X|Y ( x | y ) =
(
zero elsewhere.
0 < y < 1.
f X, Y (x,y )
3x 2
=
,
f Y (y)
1 y 6
y 2 < x < 1.
Find E
STAT 409
Spring 2012
Homework #12
(due Friday, April 20, by 3:00 p.m.)
1 5.
Let the joint probability density function for ( X , Y ) be
f ( x, y ) =
1.
x+ y
3
0 < x < 2, 0 < y < 1,
,
zero otherwise.
a)
Find the probability P ( X > Y ).
b)
Find the margina
STAT 408
Spring 2012
Homework #8
(due Friday, March 16, by 3:00 p.m.)
8th edition (
From the textbook:
1.
3.6-6
2.
3.6-14
(
)
(
)
)
3.
10.5-2
(
)
= E ( X ) = 17,
a)
2 = Var ( X ) = 298 17 2 = 9.
P ( 10 < X < 24 ) = P ( X 17 < 7 ) 1
b)
P( X <
By Chebys
STAT 408
Spring 2014
Homework #4
(due Friday, February 21, by 3:00 p.m.)
No credit will be given without supporting work.
1 3.
Alex sells Exciting World of Statistics videos over the phone to earn some extra
cash during the economic crisis. Only 10% of al
STAT 408
Spring 2015
A. Stepanov
Homework #8
(due Friday, April 3, by 3:00 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 without supp
STAT 408
Homework #7
Spring 2015
A. Stepanov
(due Friday, March 20, by 3:00 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 without sup
STAT 408
Spring 2015
A. Stepanov
Homework #9
(due Friday, April 10, by 3:00 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 without sup
STAT 409
Spring 2012
Homework #11
(due Thursday, April 12, by 4:30 p.m.)
1.
5.1-5 (
)
The p.d.f. of X is f X ( x ) = x
1
, 0 < x < 1, 0 < < . Let Y = 2 ln X.
How is Y distributed?
a)
Determine the probability distribution of Y by finding the c.d.f. of Y
F
STAT 408
Spring 2014
Name
Version A
ANSWERS
.
NetID _
Quiz 2
(10 points)
Be sure to show all your work; your partial credit might depend on it.
No credit will be given without supporting work.
1.
How much wood would a woodchuck chuck if a woodchuck could
STAT 408
Spring 2012
Homework #5
(due Friday, February 24, by 3:00 p.m.)
1.
Suppose a discrete random variable X has the following probability distribution:
P( X = k ) =
( ln 2 ) k
k!
,
k = 1, 2, 3, .
Recall ( Homework #1 Problem 9 ): This is a valid prob
STAT 408
Spring 2015
A. Stepanov
Homework #3
(due Friday, February 13, by 3:00 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
without
Practice Problems 8
1.
Suppose that the actual weight of "10-pound" sacks of potatoes varies from sack
to sack and that the actual weight may be considered a random variable having a
normal distribution with the mean of 10.2 pounds and the standard deviat
STAT 408
Spring 2015
A. Stepanov
Homework #4
(due Friday, February 20, by 3:00 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 without
STAT 408
Spring 2014
Homework #4
(due Friday, February 21, by 3:00 p.m.)
No credit will be given without supporting work.
1 3.
Alex sells Exciting World of Statistics videos over the phone to earn some extra
cash during the economic crisis. Only 10% of al
Math 408, Actuarial Statistics I
A.J. Hildebrand
General Probability, III: Bayes Rule
Bayes Rule
1. Partitions: A collection of sets B1 , B2 , . . . , Bn is said to partition the sample space
if the sets (i) are mutually disjoint and (ii) have as union th
1.
a)
1.1-7
1.2-9
Given that P ( A B ) = 0.76 and P ( A B' ) = 0.87, find P ( A ).
b)
2.
Suppose also that P ( B ) = 0.54. Find P ( A B ).
Suppose
P ( A ) = 0.40,
P ( A B ) = 0.19,
P ( B ) = 0.34,
P ( A C ) = 0.25,
P ( C ) = 0.55,
P ( B C ) = 0.17,
P ( A
1.
a)
2.6-2
2.6-2
2.6-2
Let X have a Poisson distribution with variance of 3. Find P ( X = 2 ).
b)
2.6-4
2.6-4
2.6-4
If X has a Poisson distribution such that 3 P ( X = 1 ) = P ( X = 2 ), find P ( X = 4 ).
2.
Suppose that number of accidents at
the Monstr
STAT 408
Examples for 2.3
The k th moment of X (the k th moment of X about the origin), k , is given by
k = E( X k ) =
x k f (x )
all x
The k th central moment of X (the k th moment of X about the mean), k' , is given by
k' = E ( ( X ) k ) =
( x ) k f
STAT 408
Examples for 3.2 (2)
Gamma Distribution:
f (x ) =
f (x ) =
x 1 e x ,
( )
0x<
1
x 1 e x ,
()
0x<
E(X) =
E(X) =
Var ( X ) =
,
/
Var ( X ) =
2
/2
If T has a Gamma ( , = 1 ) distribution, where is an integer, then
/
F T ( t ) = P ( T t ) = P ( X
STAT 408
Examples for 2.6
Poisson Distribution:
X = the number of occurrences of a particular event in an interval of time or space.
P( X = x ) =
x e ,
x!
E( X ) = ,
Table III ( pp. 490 492 )
EXCEL:
x = 0, 1, 2, 3, .
Var( X ) = .
gives
P( X x )
= POISSON(