HW 2
STAT 544, Fall 2015
Each homework assignment will be worth 20 points, and your best 10 of 12 assignment scores will be averaged
to determine the homework contribution to your overall course average.
Note: Five of the of the eight parts below will be
HW 12
STAT 544, Fall 2015
1) Imagine that the couples are labeled 1 through 5. Letting Aj be the event that the wife of the jth couple
is seated next to the husband of the jth couple, B0 be the event that the jth and kth husbands are seated
next to one an
Solutions for HW 10
STAT 544, Fall 2015
1) For the case of 0 = 1, for the joint pmf of X and Y we have
16/81, y cfw_0, 1,
pX,Y (0, y) = 4/81, y = 2,
0,
otherwise.
From the 4th and 5th lines of the solutions to part 1(a) of HW 9, it follows that pX (0) =
Solutions for HW 6
STAT 544, Fall 2015
1) Letting N (10) be the number of false alarms that will occur during the 10 day period, N (10) is a Poisson
random variable having mean
1
10 days = 2,
5 days
and the desired conditional probability is
P (N (10) =
Solutions for HW 11
STAT 544, Fall 2015
1) Letting y1 = g1 (x1 , x2 ) = x1 + x2 and y2 = g2 (x1 , x2 ) = x1 /(x1 + x2 ), we can solve these for x1 and
x2 , obtaining x1 = y1 y2 and x2 = y1 y1 y2 . (Note that if you multiply the two expressions (in terms
o
Solutions for HW 7
STAT 544, Fall 2015
1)
(a) The support of V = 1/U is (6, 3), and so fV (v) = 0 for v 6 (6, 3). For v (6, 3), we have
FV (v) = P (V v)
= P (1/U v)
= P (U 1/v)
Z 1/6
=
6 du
1/v
1/6
= 6u|1/v
= 1 6/v,
and
fV (v) =
d
(1 6/v) = 6/v 2 .
dv
So,
Solutions for HW 8
STAT 544, Fall 2015
1) Noting that we have
FX (x) = P (X x) = ([x X ]/X ) = ([x 2]/3),
for the desired probability we have
P (1/X < 1/2) = P (X < 0) + P (X > 2)
= P (X 0) + 1 P (X 2)
= ([0 2]/3) + 1 ([2 2]/3)
= (2/3) + 1 1/2
= (2/3) + 1
Probability Exam Questions with Solutions
by Henk Tijms1
December 15, 2013
This note gives a large number of exam problems for a rst course in probability. Fully worked-out solutions of these problems are also given, but of
course you should rst try to so
Name: Date: Period:
CCGPS Analytic Geometry
Notes: Fundamental Counting Principle Tues Mar 24 2015
Homework: Set A, Page 340: #2 — 10 even and #11
Set B, Page 341: #2 — 8a even (omit 8b)
Essential Question: How can you use the tree diagrams and the coun
UDE, Fakultt f r Mathematik: Discrete Mathematics (C1) [Balls to Boxes]
a u
1
1
Count the number of possibilities
to put k balls into n boxes
1.1
Balls distinguishable, boxes distinguishalbe
1.1.1
No restriction
Assume the balls and boxes are numbered. Th
PERMUTATIONS AND COMBINATIONS
A. PERMUTATIONS
1. A nickel and a dime are tossed on a table. In how many ways can they fall?
2. If all questions answered in a true-false quiz of ten questions, how many ways are there of
answering the entire quiz?
3. How ma
Distribution Problems
The property that characterizes a distribution (occupancy) problem is that a ball (object) must go into
exactly one box (bin or cell). This amounts to a function from balls to bins.
n distinguishable boxes
empty box allowed
no box em
HW 2
STAT 544, Spring 2014
Each homework assignment will be worth 25 points, and your best 10 of 12 assignment scores will be
averaged to determine the homework contribution to your overall course average. Typically, each assignment
will consist of from 5
HW 3
STAT 544, Fall 2015
Each homework assignment will be worth 20 points, and your best 10 of 12 assignment scores will be averaged
to determine the homework contribution to your overall course average.
Note: Five of the of the seven parts below will be
HW 1
STAT 544, Fall 2015
Each homework assignment will be worth 20 points, and your best 10 of 12 assignment scores will be
averaged to determine the homework contribution to your overall course average. Typically, each assignment
will consist of from 5 t
HW 4
STAT 544, Fall 2015
Each homework assignment will be worth 20 points, and your best 10 of 12 assignment scores will be
averaged to determine the homework contribution to your overall course average. Typically, each assignment
will consist of from 5 t
Solutions for HW 9
STAT 544, Fall 2015
1)
(a) Due to independence, the probability that both British cannons are successful, and X takes the value 2,
is (1/3)(1/3) = 1/9. And in this case, Y must be 0, since both French cannons will have been eliminated,