1
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 101.
Write each answer very clearly below the corresp
April 2005
MATH 302 Section 201
Name:
1
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 second denomination. [5] b) What is the probability of
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 Chebychevs inequality to bound the probability P (275 R 28
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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),
i. We have that P (X Y = 0) = 1/2 (because this only
1
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 each.
Write each answer very clearly below the corres
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 arrange 3 novels, 2 math books and 1 chemistry
book in a she
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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 each (102 points total).
Write each answer very clearl
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 weight 17 points each (102 points total).
Write each answe
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 ) = P (X = a1 )P (Y = a2 ).
(b) How many quadruples (w,
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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)nk .
(b) Suppose that X is a r.v. receiving the values
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 = 1
0
[
]1
1
So E[Y ] = 1/2 and E[X] = 0 x ln(x) = x2
1
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 102 points.
Write each answer very clearly below the