Conditional Probability
STA 281 Fall 2011
1 Definition
Often we are only interested in particular rows or columns of a probability table. Consider the
newspaper example, and the question Of those that receive the morning paper, what proportion receive
the
Homework 7
STA 281 Fall 2011
1
A sample of 103 galaxies located in the galaxy cluster A2142 had a mean velocity of
kilometers per second (km/s) and a standard deviation of
km/s. Suppose your goal is to
make an inference about the population mean light ve
Confidence Intervals and Hypothesis Tests
STA 281 Fall 2011
1 Background
The central limit theorem provides a very powerful tool for determining the distribution of sample
means for large sample sizes. In particular, if X1, , Xn are independent and identi
Mathematical Probability
STA 281 Fall 2011
1 Introduction
Engineers and scientists are always exposed to data, both in their professional capacities and in everyday
activities. The discipline of statistics provides methods for organizing and summarizing d
HOMEWORK 5
Due: Oct. 15
STA 281, Fall 2016
The following problems are drawn from exercises in Ch.3 of the text.
1) # 7. For each random variable defined here, describe the set of possible values for the
variable, and state whether the variable is discrete
HOMEWORK 8
Due: Nov.5, 2016
STA 281, Fall 2016
The following problems are drawn from exercises in Ch.4 & Ch.5 of the text.
1) (#59) Let X= the time between two successive arrivals at the drive-up window of a local
bank. X has an exponential distribution w
HOMEWORK 5
Due: October 15
STA 281, Fall 2016
ANSWERS
The following problems are drawn from exercises in Ch.3 of the text.
1) # 7. For each random variable defined here, describe the set of possible values for the
variable, and state whether the variable
HOMEWORK 8
Due: November 5
STA 281, Fall 2016
The following problems are drawn from exercises in Ch.6 & Ch.7 of the text.
1. ( #1)Consider a normal population distribution with the value of known.
a. What is the confidence level for the interval x 2.81 /
HOMEWORK 6
Due: October 22
STA 281, FALL 2016
The following problems are drawn from exercises in Ch.3 of the text.
1)
2)
#49. A company that produces fine crystal knows from experience
that 10% of its goblets have cosmetic flaws and must be classified as
HOMEWORK 7
Due: October 29
STA 281, Fall 2016
The following problems are drawn from exercises in Ch.3 & Ch.4 of the text. Please feel free to
use the relevant apps.
1) (#32 Ch.4) Suppose the force acting on a column that helps to support a building is a n
HOMEWORK 6
Due: October 22
STA 281, Fall 2016
ANSWERS
The following problems are drawn from exercises in Ch.3 of the text.
1)
#49. A company
that produces fine crystal knows from experience
that 10% of its goblets have cosmetic flaws and must be classifie
Homework 6
STA 281 Fall 2011
1
The National Institute for Occupational Safety and Health (NIOSH) recently completed a study to
evaluate the level of exposure of workers to the chemical dioxin, 2,3,7,8-TCDD. The distribution of
TCDD levels in parts per tri
Homework 5
STA 281 Fall 2011
1
Let X be a continuous random variable with density ( )
a. Use the pdf to find P(0.2 X < 1.5).
b. Calculate E[X].
c. Calculate V[X].
2
Let X be a continuous random variable with density ( )
a. Find the cdf of X.
b. Using the
Homework 4
STA 281 Fall 2011
1
A toll booth costs 1 dollar for cars and 2 dollars for trucks. Suppose that 30% of the vehicles
passing through the booth are trucks. Suppose we observe the next 50 vehicles and observe
whether they are cars or trucks, and t
Continuous Distributions, Mainly the Normal Distribution
STA 281 Fall 2011
1 Continuous Random Variables
Discrete distributions place probability on specific numbers. A Bin(n,p) distribution, for example, has
possible values 0, 1, , n and each of these nu
Discrete Distributions
STA 281 Fall 2011
1 Introduction
Previously we defined a random variable to be an experiment with numerical outcomes. Often different
random variables are related in that they have the same sample space or the same form for the
prob
Discrete Random Variables
STA 281 Fall 2011
1 Introduction
When we introduce probability, we said we had a sample space S which contained every possible
outcome of a random experiment. For a coin flip, the sample space might be S = cfw_Heads, Tails. It is
Distribution of the Sample Mean
STA 281 Fall 2011
1 Introduction
We define a set of random variables X1, , Xn to be a random sample from a population if all the Xi are
independent and each Xi has the same distribution. Our goal in this handout is to descr
Homework 1 Solutions
STA 281 Fall 2011
1
A university plans on conducting a survey of its recent graduates to determine information on their
yearly salaries. It randomly selected 200 recent graduates and sent them questionnaires dealing
with their present
Homework 1
STA 281 Fall 2011
1
A university plans on conducting a survey of its recent graduates to determine information on their
yearly salaries. It randomly selected 200 recent graduates and sent them questionnaires dealing
with their present jobs.
a.
Homework 3
STA 281 Fall 2011
1
Let X have the following distribution
x
p(x)
1
0.02
a.
b.
c.
d.
5
0.41
10
0.21
50
0.08
100
0.28
What is P(X>4|X50)?
Compute E[X].
Compute E[ ].
Compute V[X].
2
Suppose X is a random variable with E[X]=4 and V[X]=9. Let Y=4X+
HOMEWORK 7
Due: October 29
STA 281, FALL 2016
The following problems are drawn from exercises in Ch.3 & Ch.4 of the text. Please feel free to
use the relevant apps.
1) ( #2 Ch.4) Suppose the reaction temperature X (in C0 ) in a certain chemical process ha