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Math 302 midterm
Instructor: Asaf Nachmias
Duration: 50 minutes.
Instructions:
Write your name and student ID on every page.
This examination contains four questions. The total number of points is
April 2005
MATH 302 Section 201
Name:
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1) A poker hand consist of 5 cards out of a deck of 52. a) What is the probability of a Full House, that is, three cards of one denomination and two cards of a
Math 302 solutions to Assignment 10
1. (25 pts) Let X1 , X2 , . . . , X100 be i.i.d. random variables each equal 2 with probability .8 and
1 with probability .2. And write R = X1 X2 X100 .
(a) Use Che
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Math 302 Solutions to practice nal 1
1. (a) A, B, C are independent events if all of the following occur:
P (A B) = P (A)P (B),
P (B C) = P (B)P (C),
P (A C) = P (A)P (C),
P (A B C) = P (A)P (B)P (C
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Math 302 practice midterm
Instructor: Asaf Nachmias
Duration: 50 minutes.
Instructions:
Write your name and student ID on every page.
This examination contains four questions with weight 25 points
1
Math 302 midterm solutions
1. (a) (9 pts) Carefully dene (with a formula) what it means for two events A and B to
be independent.
P (A B) = P (A) P (B) .
(b) (9 pts) How many ways are there to arran
1
Math 302 Practice Final 1
Instructor: Asaf Nachmias
Duration: 2.5 hours .
Instructions:
Write your name and student ID on every page.
This examination contains six questions with weight 17 points
1
Math 302 Practice Final 2
Instructor: Asaf Nachmias, section 102
Duration: 2.5 hours .
Instructions:
Write your name and student ID on every page.
This examination contains six questions with weig
1
Math 302 solutions for practice midterm
1. (a) Carefully dene (with a formula) what it means for two discrete r.v.s X and Y to
be independent.
For any two numbers a1 , a2 we have P (X = a1 , Y = a2
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Math 302 solutions to practice nal 2
1. (a) Let X be a binomial r.v. with parameters n and p. Write the probability mass
function of X.
For any k = 0, 1, . . . , n we have P (X = k) =
(n )
k
pk (1 p
Math 302 solutions to assignment 9
1. (20 pts) In order to calculate E[X], E[Y ] we calculate the marginal densities rst.
1
fX (x) =
f (x, y)dy = ln(x) = ln(x1 )
0 x 1.
x
fY (y) =
y
0 y 1.
f (x, y)dx
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Math 302 Final Exam
Section: 101
Instructor: Ed Perkins
Duration: 2.5 hours .
Instructions:
Write your name and student ID on every page.
This examination contains eight questions worth a total of