Basic Principle of Counting - if 1 experiment can result in m
outcomes & another can result in n, there are mn total outcomes
Permutations - arrangement of objects. There are n! ways of
arranging n objects. Ex permutation with grouping. 4 math
NOTES ON RANDOM VARIABLES AND THEIR DISTRIBUTIONS by A. Ledoan In the first three chapters of his book  Ross sets forth the formulation of probability theory. The idea of an experiment, a sample space corresponding to the experiment, and events in
Introduction to Probability Lecture Notes
Version July 28, 2016
David F. Anderson
c Copyright 2016 David F. Anderson, Timo Seppalainen and Benedek Valko
Random outcomes and random variables
Math 201 - Homework 5
(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
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
Let X have the density function
2x, if 0 < x < 1,
fX (x) =
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
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
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
(a) Find the cumulative distribution function of X.
(b) Use part (a) to
Math 201 - Homework 8
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
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
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
HOMEWORK #1 MTH 201, FALL 2007 DUE: WEDNESDAY, SEPTEMBER 19, IN-CLASS AT THE BEGINNING OF CLASS The following problems are numbered the same in both the 6th and 7th edition of Ross's textbook. Chapter 1, Problems: 13, 22; Chapter 1, Theoretical Exe
NOTES ON CONDITIONAL PROBABILITY, BAYES' THEOREM, AND INDEPENDENCE by A. Ledoan The ideas of conditional probability and independence play a central role in the study of random phenomena. Conditional probability is the study of how additional informa