STATISTICS 301
HOMEWORK 5 Solution
thet
(a)meanof X = 2.5 + 3 .3 + 4 .1 + 5 .05 + 6 .05 = 2.85 days
(b) P [X 3] = f (2) + f (3) = .5 + .3 = .8
(c) The delivery times for the two letters should be independent since they were mailed a
very dierent times.
P
STATISTICS 301
HOMEWORK 6 Solution
2.2 (a) The function is non-negative and the area of the rectangle is .52=1. It is a probability density function.
(b) Since f (x) takes negative values over the interval from 1 to 2, it is not a probability
density func
Solutions to Homework 4
CHAP 4:
5.4 (a) Because P (AB ) + P (AB ) = P (B ), we have P (AB ) = .32 .20 = .12. Likewise,
) = P (A) P (AB ) = .45 .12 = .33. Also, P (A) = 1 P (A) = 1 .45 = .55.
P (AB
P (AB ) = P (A) P (AB ) = .55 .20 = .35.
A
A
(b) P (A|B )
Solutions to Homework 3
2.11 (a) The tree diagram is given in Figure 1.
Figure 1: Tree diagram of 2.11
S = cfw_HHH, HHT, HT H, HT T, T HH, T HT, T T H, T T T .
(b) Assuming the coins are fair, all the elementary outcomes are equally likely.
1
P (HHH ) = P
Solutions to Homework 2
3.21 (a) The class intervals have unequal widths so the rectangles have height=(relative
frequency)/(width of interval). For the interval 0 to 25, height = (10/84)/25 = .00476. For
the interval 100 to 150, height = (7/84)/25 = .001
Ismor Fischer, 1/11/2014
2.5-1
2.5 Problems
1.
Follow
the
instructions
in
the
posted
R
code
folder
(http:/www.stat.wisc.edu/~ifischer/Intro_Stat/Lecture_Notes/Rcode/) for this problem, to
reproduce the results that appear in the lecture notes for the Memo
Ismor Fischer, 8/5/2012
2.3-1
2.3 Summary Statistics Measures of Center and Spread
Distribution of X
X discrete
X continuous
?
POPULATION
Random Variable X,
numerical
?
True center = ?
True spread = ?
parameters
(population characteristics)
unknown fixe
Solutions to Homework 7
CHAP 6:
5.4 The standardized variable is Z =
X 100
.
3
(a) From the normal table we nd P [Z < .84] = .7995. Therefore,
b = 110 + 3(.84) = 112.5.
b110
3
= .84, so
(b) Here P [X < b] = 1 .001 = .999. From the normal table, we nd P [Z
Solutions to Homework 1
Part 1
8.5 The newspaper is suggesting that the statistical population is the collection of preferences
for each adult in the city while the sample is the collection of preferences of the particular
persons who sent in their votes.
Problem 5 (20 pts)
0.10
0.00
0.05
fx
0.15
0.20
(b) (12 pts) The time for an emergency squad to arrive at the sports center is distributed as a
normal variable with mean = 15 minutes and standard deviation = 2 minutes. Which
arrival period with shortest du
STATS 301 QUIZ #3 NAME WEE"
Discussion Section #
1. 2 pts) Would you expect a positive, negative, or nearly zero correlation for the following. Give a reason for your
answer.
The number of songs downloaded from the Internet last month and thenumber of h
Stat 301 Lecture 5&6, Spring 2011
Sample Final Exam
(Total : 100 points)
(Solution)
Name :
Student ID :
Disc. Sec. :
Problem
Max Points
Your Score
1
20
2
10
3
20
4
20
5
10
6
20
Total
100
Problem 1 (20 pts) Here is the assignment of probabilities that desc
Stat 301 - Lecture 5 & 6
First Midterm Sample Exam
(Total: 100 points)
Name :
Student ID :
Disc. Sec. :
Problem
Max Points
Your Score
1
20
2
20
3
20
4
20
5
20
Total
100
Problem 1 (20 pts) A student collected a sample of approximate times (minutes) of 20 f
CHAPTER 4
4.1 - Discrete Models
General distributions
Classical: Binomial, Poisson, etc.
4.2 - Continuous Models
General distributions
Classical: Normal, etc.
~ The Normal Distribution ~
(a.k.a. The Bell Curve)
standard
deviation
X ~ N(, )
Johann Ca
Imagine the following observational study
X = Survival Time (Time to Death) in two independent normally-distributed populations
SMOKERS
X1 ~ N(1, 1)
1
NONSMOKERS
X2 ~ N(2, 2)
2
Null Hypothesis
H0: 1 = 2, i.e.,
1 2 = 0
(No mean difference")
Test at signif
Power and Sample Size
IF the null hypothesis H : =
is true,
then we should expect a random sample
mean to lie in its acceptance region with
probability 1 , the confidence level.
That is,
P(Accept H0 | H0 is true) = 1 .
0
0
Therefore, we should expect a
Overview of Biostatistical Methods
Overview of Biostatistical
Methods
~ GOLD STANDARD ~
Designed to compare two or more treatment
groups for a statistically significant difference
between them i.e., beyond random chance
often measured via a p-value (e.g.
CHAPTER 7
Linear Correlation & Regression Methods
7.1 - Motivation
7.2 - Correlation / Simple Linear Regression
7.3 - Extensions of Simple Linear Regression
Parameter associationvia SAMPLE DATA
Testing for Estimation between two POPULATION variables X