Stats 120A Homework 9 Solutions
This homework assignment is worth a total of 22 points. Problems marked with
an asterisk (*) are graded based on correctness. The remaining problems are graded
based on completion (full credit as long as you completed the p
Hypergeometric Distribution
Finite population generalization of Binomial Distribution
Population:
N Elements
k Successes (elements with characteristic if interest)
Sample:
n Elements
Y = # of Successes in sample (y = 0,1,min(n,k)
k N k
y n y
p( y)
Math 461
Introduction to Probability
A.J. Hildebrand
Conditional Probability
Denition and properties
1. Denition: The conditional probability of A given B is denoted by P (A|B) and
dened by the formula
P (AB)
,
P (A|B) =
P (B)
provided P (B) > 0. (If P (B
Negative Binomial Distribution Example
A pediatrician wishes to recruit 5 couples, each of whom is expecting
their first child, to participate in a new natural childbirth regimen. Let p
= P(a randomly selected couple agrees to participate).
If p = .2, wha
Solutions to selected problems in chapter 2.3
Math 362, Spring 2011
Grethe Hystad
Exercise 2.12 On a large college campus, 84% of the students report drinking alcohol within
the past month, 33% report using some type of tobacco product within the past mon
The FIFTEEN QUESTIONS follow
1) Five cards are dealt, what is the probability that the 5th one is a king?
[4/52]
2) Five cards are dealt, what is the probability that the 5th one is a king, given that the first four are queens?
[4/48]
3) Five cards are de
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STAT120B Practice Final
1. True or false (You do NOT need to justify your answer)
a) The significance level of a test is equal to the probability that the null hypothesis is true.
b) The probability that the null hypothesis is falsely rejected is equal to
Dr. Neal, WKU
MATH 329
Law of Total Probability
and Bayes Rule
Law of Total Probability: Suppose events A1 , A2 , . . . , An form a partition of . That
is, the events are mutually disjoint and their union is all of . Then for any other event
B , we have
P
page 1
110SOR201(2002)
Chapter 1
Basic Probability Concepts
1.1
Sample and Event Spaces
1.1.1
Sample Space
A probabilistic (or statistical) experiment has the following characteristics:
(a) the set of all possible outcomes of the experiment can be describ
Multiple random variables
N -dimensional random vector (i.e., vector of random variables) is a function from the sample
space to RN (N -dimensional Euclidean space).
Example: 2-coin toss. = cfw_HH, HT, T H, T T .
Consider the random vector X =
X1
X2
, whe
Two-Sample Problem for
Testing Equal Means
Stats 120B
Feb 27, 2015
One-sample problem
A sample 1 , 2 , , is drawn from the
distribution (, 2 )
is the parameter of interest
An estimator for , =
~ ,
2
1
=1
One-sample problem
Construct a 1 100% level co