Midterm 3 Solutions
Math 50101, Spring 2005
1. Let X denote a random variable whose probability density function (pdf) is given by
f (x) = c|x|3 ,
|x| > 1.
(a) Plot f , and find c.
Solution: To find c compute
it equal to one, viz.,
Z
1 = 2c
R
f (x) dx an
Quiz 6 (Mar. 3, 2014), Math 5010
Name:
NO WORK means NO POINTS!
1. (5 pt) Suppose the time (in hours) required to repair a machine is an exponentially
distributed random variable with parameter = 2 (i.e. the pdf is f (x) = 2e2x for x 0
and 0 otherwise).
(
Quiz 7 (Mar. 17, 2014), Math 5010
Name:
NO WORK means NO POINTS!
1. Let X be a standard normal random variable, i.e., the pdf of X is f (x) =
(a) Find the probability density function of Y = eX .
(b) Find the probability density function of Y = X 2 .
2
1
Quiz 8 (Mar. 24, 2014), Math 5010
Name:
NO WORK means NO POINTS!
1. (2pt) Let X be a standard normal random variable, i.e., the pdf of X is f(x)
for x e R. Write the expectation of X as some integral then find the expectation.
Q
-fc
ciidy j(
2. (3pt) Let
Name:
Quiz 10 (April. 14, 2014), Math 5010
NO WORK means NO POINTS!
1. (5pt) Let (X, Y) have joint pdf f(x, y) = 2(x + y) if 0 < x < y < 1, and 0 otherwise.
Let Z = XY. Find the pdf of Z. i.e., find fxy.
UK
/U
(:). !/
U
1
(v)
(e)
C-f
Quiz 11 (April. 21, 2
Exam 1
Math 5010
February 19, 2014
NAME:
(Please Print)
DIRECTIONS:
Do each of the problems and show fl
your
work.
NO WORK means NO POINTS!
No Calculators, No Celiphone, No Comupters!
No Cheating!
Box or circle and LABEL
your
final solution.
Raise y
Exam 2
Math 5010
April 7, 2014
NAME:
(Please Print)
DIRECTIONS:
Do each of the problems and show all your work.
NO WORK means NO POINTS!
No Calculators, No Celiphone, No Comupters!
No Cheating!
Box or circle and LABEL your final solution.
Raise your
1. (8 pts) Find the probability that a five-card poker hand (i.e. 5 out of
a 52-card deck) will be:
(a) Four of a kind, that is four cards of the same value and one card
of a different value (xxxxy shape).
(b) Full house, that is 3 cards of the same value
Class Information
Midterm Exam:
May review the exam in my office during my office
hours!
Note: AS of April 14: I will open up more office
hours.
Thursdays: 2-5 (Open Appointment)
Up to 4 students at a time can come in to review exam
Tuesdays: 3-5:15 (
Caption Contest
1. Select ONE of the three pictures provided above.
2. Fill in the bubbles, if you select Picture 1 or 2, OR write a caption at the bottom of
Picture 3. The bubble topics or caption MUST relate to a topic we have studied this
semester.
Duties of Agent to Principal
Expressed
Implied by Law
Duty of Obedience
Duty of Good Conduct
Duty of Diligence care, competence, and diligence
Duty to Inform
Duty to Account
Fiduciary Duty:
Conflicts of Interest
Self-Dealing
Duty Not to Compete
Mi
Quiz 3 (Feb. 3, 2014), Math 5010
Naine:
NO WORK means NO POINTS!
1. (10 1)1) Suppose tWo cards Ironi a staiiclaid deck of 52 cards are missillg (equally likely).
Now we draw one card. Find the probability that the randomly drawn card is a Heart by
using t
Solutions to Midterm #1
Mathematics 50101, Spring 2006
Department of Mathematics, University of Utah
1. When you walk into a certain sandwich shop, you will be asked, Would like it on wheat or
white bread? After you answer, then you are asked, Would you l
Midterm 1 Solutions
Math 50101, Spring 2005
1. A pizzeria advertises that it offers over 1000
varieties of pizza. Suppose that you can order
any combinations of pepperoni, mushrooms,
sausage, green peppers, onions, anchovies,
salami, bacon, olives, and gr
Solutions to Midterm #2
Mathematics 50101, Spring 2006
Department of Mathematics, University of Utah
1. An urn contains R red balls and W white balls, where R and W are strictly positive
integers. Balls are drawn at random one after another. Every time a
Solutions to Midterm 2
Mathematics 5010001, Summer 2009
1. There are 2 red bottles and 3 green bottles in a basket. We select a bottle at random, independently, until we sample a red bottle. Compute the mass function of
X, where X denote the sample size r
Solutions to Midterm 2
1. A pair of fair dice are cast, and the number of rolled dots, on each die, is
recorded. Let X denote the sum of the two numbers. Find the probability
mass function of X.
Solution. Here is the table for the mass function:
x
2
3
4
5
Midterm 2 Solutions
Math 50101, Spring 2005
1. An urn contains R red balls and W white balls, where R
and W are strictly positive integers. Balls are drawn at
random one after another. Every time a ball is drawn,
it is replaced back in the urn together wi
Midterm 3 Solutions
Math 50101, Spring 2005
(a) Compute C.
Solution: We have
Z Z 2x
1. Let > 0 be a fixed number. Recall that the pmf for a
Poisson() random variable is: p(k) = e k /k! for k =
0, 1, 2, . . . .
Now suppose X and Y are independent, each is
Solutions to Midterm #3
Mathematics 50101, Spring 2006
Department of Mathematics, University of Utah
1. A continuous random variable X has density function f given by the following:
x
Ce , if x 0,
f (x) =
0,
otherwise.
(a) Compute C.
R
Solution: 1 = C 0
Solutions to Midterm #4
Mathematics 50101, Spring 2006
Department of Mathematics, University of Utah
April 7, 2006
1. A random vector (X , Y ) has the following (joint) mass function p(x , y) = P cfw_X = x , Y = y:
y \x
1
2
3
1
1/3
1/9
1/27
2
10/27
1/27
1
Solutions to Midterm 1
Math 5010-1, Spring 2007, University of Utah
1. In 2005, the United Nations reported that approximately 50.74 percent of
the adults in the US are women. Suppose we take a random sample of 100
people, without replacement, from this p
Leasehold Estate - Transfer
Transfer of Interests: Absent a restriction in
agreement, both Landlord and Tenants interest may
be transferred.
Landlords Transfer of Interest:
Interests:
Revisionary ownership interests AND right to rent
New owner takes pr