MATH 351
Solutions # 7
1. Suppose that X is a normal random variable with parameters = 1
and 2 = 9.
(a) Find P cfw_2 X 1
Solution. Since X N(1, 9), we we have (X 1)/3 is standard
normal, i.e. Z = (X 1
Fall 2013, Math 351,
Quiz 2, 9/3/2011
Name
Puid
Let k be a parameter. Consider the following system in unknowns x, y, z
x+yz =1
2x + 3y + kz = 3
x + ky + 3z = 2
A. (5 pt) prove that if k = 2 then the
MATH 351
Solutions #1
1. How many dierent 8-digit reservation codes by an airline are possible
if the rst two places are occupied by letters, the next three places are
occupied by numbers, the sixth p
MATH 351
Solutions #5
1. Let X be a Bernoulli random variable with parameter p = 5 . Find
6
E[cos(X)], E[3X ], and E[tan1 (X)].
Solution.
E[cos(X)] =
x:p(x)>0
5
1 5
2
1
g(x)p(x) = cos(0)( )+cos(1)( )
MATH 351
Solutions #6
1. Suppose
c(1 x2 ) if 2 x 2
0
otherwise.
f (x) =
Is there a value of c for which f is a probability density function? Why
or why not?
Solution. This cannot be a probability dens
MATH 351
Solutions #2
1. Two dice are thrown. Let E be the event that the sum of the dice is
even, let F be the event that at least one of the dice lands on 6 and
let G be the event that the numbers o
Fall 2013, Math 351, Section 154
Quiz 9, 11/21/2011
Name
Puid
Problem 1 (2 pt). Consider the system
x1 + 3x3 = 0,
2x1 + x2 + x3 = 5
3x1 + 2x2 + x3 = 4.
Use Carmers Rule to compute x3 .
Solution
The sy
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page 1o16
Math 35L, Probability
Exam 1
October 4,2OL2
Directions. Please write your narne at the top of the page. Your answers should be in simplest form
possible without a calculator. You ma
Math 351, Probability
Solutions 3
1. If the letters of the word GOLDIN are arranged randomly in a row,
what is the probability that none of the letters in the chosen word is
in the same position in wh
MATH 351 Solutions # 4
October 3, 2012
1. THIS QUESTION DID NOT HAVE ENOUGH INFORMATION. I WILL ASSUME THAT,
FOR ANY RANDOM LETTER, THERE IS A 50/50 CHANCE ITS FROM A MALE OR A
FEMALE. You get two let