MA 485-1D (Probability), Dr. Chernov
Show your work. 9 problems. Total is 100 points.
Final Exam
Fri, Dec 5, 2008
1. (10 pts) Let X be an exponential random variable with mean 100.
(a) Use Markovs inequality to obtain an upper bound on P(X 300).
Answer: P
Exercises in Probability Theory
#1, due on Tuesday, January 24
Ioulia Karpechina, MA 485/585, Spring 2017
Based on Materials by Nikolai Chernov
Instructions: Answers to homework problems should generally not only
include the numerical result, but also a s
Exercises in Probability Theory
Ioulia Karpechina, MA 485/585, Spring 2017
Based on Materials by Nikolai Chernov
Instructions: Answers to homework problems should generally not only
include the numerical result, but also a sufficient amount of explanation
MA485/585, Probability
February 10, 2015
Dr. Li
Name and section:
1. Do not open this exam until you are told to do so.
2. This exam has 8 pages including this cover. There are 7 questions, for a total of 110
points. Note that the problems are not of equa
MA 485-1C (Probability), Dr. Chernov
5 problems, each is worth 20 points. Show your work.
Midterm test #2
Mon, Oct 31, 2011
1. Find the following probabilities for two normal random variables: Z = N (0, 1) and
X = N (1, 16).
(a) P (Z > 2.17) = Answer: 1 (
MA 485-1C (Probability), Dr. Chernov
6 problems, each is worth 17 points. Show your work.
Midterm test #1
Mon, Sep 26, 2011
1. You have three alarm clocks that will ring on any given morning with probabilities
0.8, 0.85, and 0.9, respectively. To wake up
MA485/585, Probability
April 22, 2014
Dr. Li
Name and section:
1. Do not open this exam until you are told to do so.
2. This exam has 10 pages including this cover. There are 8 questions, for a total of 100
points. Note that the problems are not of equal
MA485/585, Probability
February 20, 2014
Dr. Li
Name and section:
1. Do not open this exam until you are told to do so.
2. This exam has 7 pages including this cover. There are 6 questions, for a total of 100
points. Note that the problems are not of equa
MA485/585, Probability
April 3, 2014
Dr. Li
Name and section:
1. Do not open this exam until you are told to do so.
2. This exam has 6 pages including this cover. There are 5 questions, for a total of 100
points. Note that the problems are not of equal di
MA 485-1C (Probability), Dr. Chernov
7 problems, 15 points for each. Full credit is 100 points.
Final Exam
Wed, Dec 14, 2011
1. (15 pts) Assume that customers arrive at a small store at a rate of one customer per
5 minutes (on average). John works at the
MA 485-1D (Probability), Dr. Chernov
6 problems, each is worth 17 points. Show your work.
Midterm test #1
Mon, Sep 29, 2008
1. In a class of 20 students, the math teacher selects ve students at random for a test
in math. The next day, the science teacher
MA 485-4A, Probability (Dr Chernov)
Final Exam
Thu, Dec 9, 2004
Students name
Be sure to show all your work.
Each problem is 14 points (112 total!). Full credit is given for 100 points!
1. Two random variables X and Y have joint density function f (x, y)
MA 485-4A (Probability), Dr. Chernov
Show your work. Each problem is 20 points.
Midterm test #2
Thu, Oct 28, 2004
1. Two random variables X and Y have joint density function f (x, y) = c on the rectangle cfw_0 < x < 5, 0 < y < 1 (and zero elsewhere).
(a)
MA 485-4A (Probability), Dr. Chernov
Show your work.
Midterm test #1
Tue, Sep 28, 2004
1 (12 pts). The letters s, s, s, t, t, t, i, i, a, c are arranged in a random order. What is the
probability that they will spell the word statistics?
Answer:
3! 3! 2!
MA 485-1D (Probability), Dr. Chernov
5 problems, each is worth 20 points. Show your work.
1. A continuous random variable X has distribution function
FX (x) =
x4 1
80
for
1x3
(a) Find the density function fX (x).
Answer: fX (x) = FX (x) = x3 /20, for 1 x
Probability Theory
Lecture Notes for MA 485/585, Spring 2017 (I.Karpechina)
Authored by: Nikolai Chernov
1
Combinatorics
1.1 Example. Five cards are labeled 1, 2, 3, 4, 5. They are shuffled and lined
up in an arbitrary order. How many ways can this be don