MATH355, Fall 06
EXAM
1A Key
12/10/06
1. Of 35 microcomputers available in a supply room, 20 have circuit boards for a printer, 5 have circuit
boards for a modem, and 13 have neither board. Using P to denote those that have printer boards and
M to denote
Homework #9 Solution
3.71 A warehouse contains ten printing machines, four of which are defective. A company randomly selects
ve of the machines for purchase. What is the probability that all ve of the machines are not defective?
ans: There are four machi
Homework Solution # 4
3.1 Among 10 applicants for an open position, 6 are women and 4 are men. Suppose that three applicants
are randomly selected. Find the probability distribution for X , the number of female among the nal
three.
Answer: The values for
Homework Solution # 3
2.27 Cars coming into an intersection can turn left, turn right, or go straight. Two cars enter an intersection
in succession. Find the probability that at least one of the two turns left given that at least one of
them turns. Let R
Homework Solution # 2
2.11 An experiment observes two cars in successive as they move through the intersection of two streets.
(a) All outcomes: let S, R, and L indicate the cars go straight, turn right, and turn left respectively.
Then the sample space i
Homework Solutions
2.1.
There are 10 elements in P, 5 in M, and 13 in neither P nor M. Since there are 25
computers, computers with both boards, i.e. P M, must have (10+5+13) 25 = 3.
(a) PM = 3.
(b) (PM)c = computers with neither P nor M = 13
(c) Computer
MATH355, Fall 06
EXAM
4 Key
12/1/06
1. From a group consisting of 3 Republicans, 2 Democrats, and 3 Independents, a committee of three
persons is to be randomly selected. Let X denote the number of Republicans and Y the number of
Democrats on the committe
MATH355, Fall 06
EXAM
3 Key
11/08/06
k x2 (1 x)
0
1. Suppose that a random variable X has a p.d.f. given by f (x) =
for 0 x 1 .
otherwise
(a) Find the value of k that makes this a p.d.f.
1
ans:
1
kx2 (1 x)dx = k
0
(x2 x3 )dx =
0
k
= 1. Therefore k = 12.
1
MATH355, Fall 06
EXAM
2B Key
12/09/06
1. Let Y denote a random variable that has a Poisson distribution with mean = 2.2. Find the following:
(a) P (Y = 4)
(b) P (Y 4)
ans: (a) P (Y = 4) =
e
2.2
(c) P (Y < 4)
(d) P (Y 4|Y 2)
4
(2.2)
= 0.10815
4!
ans: (b) P