Florida Atlantic University
Instructor: Hongwei Long
STA4442 Midterm Exam
May 28, 2015
No books, notes or other aids, except calculators and the provided formula
sheet, are allowed.
1. A committee of 5 people is to be selected from a group of 6 men and 9
Solutions to Assignment 6 (STA 4442)
5.1-2. Solving the equation y = x2 , we nd that x = y = v(y) (another solution
x = y is not suitable since x must be positive as given in the p.d.f. f (x) and
v (y) = 1 y 1/2 . It is easy to see that Sx = cfw_x : 0 < x
Solutions to Assignment 5 (STA 4442)
3.2-2. (a) Note that = 2/3. Then the waiting time X until the rst call that arrives
after 10am has an exponential distribution with parameter = 1/ = 3/2. Hence
the pdf of X is
2
f (x) = e2x/3 , 0 x < .
3
(b)
2 2x/3
P (
Solutions to Assignment 3 (STA 4442)
2.1-6. (a) In the random experiment of rolling a pair of fair dice, the sample space
1
consists of 36 ordered pairs and each pair has probability 36 . Let X be the sum of
the dice. Then, X can take possible values 2, 3
Solutions to Assignment 2 (STA 4442)
1041
1.3-2. (a) 1456 .
(b) 392 .
633
(c) 649 .
823
(d) The proportion of women who favor a gun law is greater than the proportion of
men who favor a gun law.
1.3-4. (a) We use H denote heart. Then, by multiplication ru
Solutions to Assignment 4 (STA 4442)
2.4-4. (a) X has a binomial distribution b(7, 0.15).
(b) (i) P (X 2) = 1 P (X 1) = 1 0.7166 = 0.2834.
(ii) P (X = 1) = 7 (0.15)(1 0.15)6 = 0.3960.
1
7
x
7x
= 0.9879.
(iii) P (X 3) = 3
x=0 x (0.15) (0.85)
2.4-6. (a) X h
Summary of Chapters Three, Four and Five (Final
Review)
Chapter 3. Continuous Distributions
A random variable X is called continuous if there is a nonnegative function f , called the probability density function of X,
such that for any set B
P (X B) =
f (
Solutions to Quiz # 1 (STA 4442)
1. Consider families that have four children each, and select one such family at random.
(a) Describe the sample space S in terms of their children as 4-tuples, agreeing, for
example, gbbb would indicate that the youngest
Review of Double Integrals
1. Functions of two variables
The temperature T at a point on the surface of the earth de
pends on the longitude x and latitude y of the point. T can be
considered as a function of the two variables 39 and y, or as a
functiQIl-
Solutions to Quiz # 4 (STA 4442)
1. Suppose that the current measuements in a strip of wire are assumed to follow a
normal distribution with mean of 12 milliamperes and a variance of 9 (milliamperes)2 .
(a) What is the probability that a measurement will
Solutions to Quiz # 3 (STA 4442)
1. Let the random variable X have a probability density function
cx2 , 0 x 2
0,
otherwise.
f (x) =
(a) Find the value of c.
(b) Find the distribution function F (x).
(c) Find = E[X] and P (X > 1).
Solution. (a) Since
f (x)
Summary of Chapter One
Sample Spaces and Events: Let S denote the set of all possible outcomes of an
experiment. S is called the sample space of the experiment. An event is a subset of S.
We introduce some important concepts like union, intersection, comp
Solutions to Quiz # 2 (STA 4442)
1. A box of candy hearts contains 52 hearts of which 19 are white, 10 are tan, 7 are
pink, 3 are purple, 5 are yellow, 2 are orange, and 6 are green. If you select 8 pieces
of candy randomly from the box, without replaceme
Solutions to Assignment 1 (STA 4442)
1.1-2. Let B be the event that a customer insures more than one car, C be the
event that a customer insures a sports car. We want to nd P (B C) ). Note that
P (B) = 0.85, P (C) = 0.23 and P (B C) = 0.17. Then, by Theor