Math 201 - Homework 5
Exercise 1.
(a) Show that if X Geom(p) then
P (X = n + k|X > n) = P (X = k), for every n, k 1.
This one of the ways to define the memoryless property of the geometric distribution. It
states the following: given that there are no suc
Math 201 - Homework 3
Exercise 1.
An urn contains b red and c green balls. One ball is drawn randomly from
the urn and its color observed; it is then returned in the urn, and additional r balls of the
same color are added to the urn, and the selection pro
Math 201 - Homework 11
Exercise 1.
Let X have the density function
(
2x, if 0 < x < 1,
fX (x) =
0,
otherwise.
and let Y be uniformly distributed on the interval (1, 2). Assume X and Y are independent.
Give the joint density function of (X, Y ). Calculate
Math 201 - Homework 10
Exercise 1.
Let X1 , X2 be independent Poisson random variables such that Xi has mean
i for i = 1, 2. Define
Y = X1 + X2 .
Show that Y is distributed Poisson with mean 1 + 2 .
You can use the following fact: if W and Z are independe
Math 201 - Homework 2
Exercise 1. May and Jonny are playing paintball in opposite teams and they try to shoot
each other simultaneously.
The probability that both May and Jonny hit the target in a single shot is 1/8.
The probability that May hits the ta
Math 201 - Homework 7
Exercise 1.
Choose a point uniformly at random from the triangle with
vertices (0, 0), (0, 30), and (20, 30). Let (X, Y ) be the coordinates of the
chosen point.
(a) Find the cumulative distribution function of X.
(b) Use part (a) to
Math 201 - Homework 8
Exercise 1.
The homework submissions to the university computer center start at midnight (00:00). The number of homework submissions between midnight and any time t > 0
afterwords is distributed Poisson with mean t, where > 0 is some
MATH 201 - INTRODUCTION TO PROBABILITY
Homework Assignment 1
(1) A fair coin is tossed 11 times. In the end of the experiment we get an ordered vector of
length 11 with elements H and T.
(a) What is the number of possible outcomes?
(b) What is the number
Math 201 - Homework 12
Exercise 1. Customers arrive to the store according a Poisson process with intensity = 1
customers per hour. Let N [0, t] be the number of arrivals between [0, t].
(a) Find the probability
P (N [0, 2] = 2, N [2, 3] = 1|N [0, 6] = 6)
Math 201 - Homework 4
Exercise 1.
Suppose that a persons birthday is a uniformly random choice from the
365 days of a year (leap years are ignored), and one persons birthday is independent of the
birthdays of other people. Alex, Betty and Conlin are compa
MTH 165 FULL REVIEW
MTH 165 Midterm 2 Outline
Vector Spaces
Rn = cfw_(x1, x2, , xn) : x1, , xn R, so the 0-vector" is (0, , 0).
Mn(R) = the set of n x n matrices with real entries, so the 0-vector" is the matrix of all zeros.
Pn(R)= the set of polynomials
MTH 165: Linear Algebra with Differential Equations
1st Midterm
October 17, 2013
NAME (please print legibly):
Your University ID Number:
Indicate your instructor with a check in the box:
Mijia Lai
Eyvindur Ari Palsson
Mihai Bailesteanu
MWF 10:00 - 10:50 A
MTH 165: Linear Algebra with Differential Equations
First Midterm
October 21, 2014
NAME (please print legibly):
Your University ID Number:
Indicate your instructor with a check in the box:
Doyle
MWF 10:25-11:15
Friedmann MW 14:00-15:15
Madhu
MW 12:30-13:4
MTH 165: Linear Algebra with Differential Equations
1st Midterm
February 21, 2013
NAME (please print legibly):
Your University ID Number:
Indicate your instructor with a check in the box:
Dan-Andrei Geba
Giorgis Petridis
Eyvindur Ari Palsson
MWF 10:00 - 1
Designed by Chris Gatmaitan
SUMMER 2016
dance
CODE
SEC L/L HOURS
217
30762
218
31128
219
DAYS
INSTRUCTOR
ROOM college
RECIPE, FORMULA, AND FOOD COSTS 1 UNIT
Development and standardization of food production
Lec 1:00-1:50 PM
MTW Martin
E
Introduction to Financial Mathematics
Kyle Hambrook
September 19, 2016
Chapter 1
Probability Theory
Financial mathematics is built on probability theory. Indeed, the following assumption is
fundamental: The value of an asset at a future time is a random v
Chapter 1
Combinations with replacement: n for 71 possibilities and 7 trials.
Permutations: n! for 71 unique objects of lm for k repetitions.
Let there be a committee of 3 men and 2 women out of 7 men and 5
women. 2 men wont sit together. Number of combin
Math 162: Calculus IIA
First Midterm Exam ANSWERS
October 15, 2015
1. (20 points)
(a) Use integration by parts to express In =
R /2
0
cosn x dx in terms of In2 for n 2.
Answer:
Solution: a.) Let u = cosn1 x and dv = cos x dx, so du = (n 1) cosn2 x sin x d
Math 162: Calculus IIA
First Midterm Exam ANSWERS
October 11, 2016
1. (20 points)
(a) Use integration by parts twice to express In =
R
xn cos x dx in terms of In2 for n 2.
Answer:
Apply integration by parts, with u = xn and dv = cos x dx and therefore du
Math 162: Calculus IIA
First Midterm Exam ANSWERS
October 16, 2014
1. (20 points)
(a) Use integration by parts to express
R
xn ex dx in terms of
R
xn1 ex dx for n > 0.
(b) Use the formula repeatedly to find
Z
x3 ex dx.
You will not get partial credit here
EXTRA CREDIT 6 SOLUTION
Question: Suppose you have two circles, one with radius r1 centered at the origin, and
one with radius r2 centered at (r1 + r2 , 0). Thus, the circles have the point P = (r1 , 0) in
common. Suppose the circle with radius r2 begins
Extra credit problem 2
Find the volumes of a regular tetrahedron, a regular octahedron and
a regular cuboctahedron (look it up), each having edges of length s.
Show that a regular cuboctahedron is the disjoint (or nonoverlapping) union of eight regular te
EXTRA CREDIT PROBLEM 3
Problem. Suppose f (t) is a function defined on some interval [a, b] whose derivative is continuous
on the same interval. Use integration by parts to evaluate the following limit:
b
Z
lim
f (t) sin(t) dt
a
Solution. Fix > 0. Do inte
Math 162, Calculus IIA
Extra Credit 5
Name:
1. (1/N+1) points) Figuring out how many spheres can be packed into a container is an important problem
with applications to such things as cell biology and the airline industry (not to mention the bowling
indus
EXTRA CREDIT PROBLEM 4
Problem. Use integration by parts to show that for all x > 0,
Z
sin t
2
0<
dt <
.
ln(1 + x + t)
ln(1 + x)
0
Solution. Use integration by parts with
1
u=
ln(1 + x + t)
dx
du =
(1 + x + t) ln(1 + x + t)2
dv = sin t dt
v = cos t
and g
Assignment 1
Name: Peiran Chen
NetID: pchen22
9/14/2016
Sect 1.1:
4
a) It is not the case that Jennifer and Teja are friends. (Jennifer and Teja are not friends.)
b) It is not the case that there are 13 items in a bakers dozen. (There are not 13 items in
Part A
i. cfw_18 points)
Canstruct a truthtable for each 0f the: fallmving ccmpmmd propmsitions and determine
wimther it is a taumlogy, coaxtradiction; or contingency.
(a) cfw_iip A cfw_11) V10 -9 f1 2. (10 points)
Determine the truth value of again Of th
1. (10 pts) Prove the following theorem:
THEOREM: If a, b, c, d are positive integers, and if all) and old, then aclbd.
Notes: (i) The notation mly means a: divides y.
(ii) Show all steps in your proof (and, as usual, Show all work). 2. (10 pts) Is the fo
Part-A
1. (20 pts)
[10 points](a) Determine if
[(10) A (1) V T) /\ q)] *+ (a V 1")
is a tautology using truth tables. Show all your work.
(b) Determine the truth value of each of these statements if the domain of each variable
consists of all real numbe
[10 points](a) Make a truth table to display the truth values of the following
compound proposition:
[(0 A 1') V op] -> [(19 V q) A or]
Is it a tautology? Show all you: work. ,cfw_
[10 points](b) Recall the following rules of inference: L M a l'diulD, 0