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)/3 N(0, 1).
P (cfw_2 X 1) = P (cfw_(2 1)/3 (X 1)/3 (1
Fall 2013, Math 351,
Quiz 2, 9/3/2011
Let k be a parameter. Consider the following system in unknowns x, y, z
2x + 3y + kz = 3
x + ky + 3z = 2
A. (5 pt) prove that if k = 2 then the system has innitely many solutions.
B. (5 pt) Find k su
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 place may be a letter or a number, and
the last two digi
c(1 x2 ) if 2 x 2
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 density function. If c = 0, then
it does not integrate 1. F
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 on the two dice are equal. Find
P (E), P (F ), P (G), P
Fall 2013, Math 351, Section 154
Quiz 9, 11/21/2011
Problem 1 (2 pt). Consider the system
x1 + 3x3 = 0,
2x1 + x2 + x3 = 5
3x1 + 2x2 + x3 = 4.
Use Carmers Rule to compute x3 .
The system can be written as Ax = b where x = (x1 , x2 , x3 )
Math 35L, Probability
Directions. Please write your narne at the top of the page. Your answers should be in simplest form
possible without a calculator. You may leave answers as fractions, differences of fractions,
Math 351, Probability
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 which it appears in GOLDIN?
Solution. Let Ei be the event
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 letters in the mail one day. The rst letter you open is fr