STAT 400
Spring 2014
Homework #6
(due Friday, March 14, by 3:00 p.m.)
No credit will be given without
supporting work.
1.
The weight of fish in Lake Paradise follows a normal
distribution with mean of 8.1 lbs and standard deviation of 2.5 lbs.
a)
What pro
Tests for Two Means
STAT 400
November 15, 2016
Remark There are many circumstances where researchers are interested in comparing the means
of two distinct groups.
The parameter of interest is the difference in two population means, 1 2 .
Let X1 N (1 , 1
Discrete Random Variables
STAT 400
January 31, 2017
Definition: The random variables X is a function that assigns a value for element s S.
X translates the domain of S into numeric values, cfw_x : X (s) = x, s S.
Definition: Let S have a countable number
Expectation
STAT 400
January 31, 2017
Definition: Mathematical expectation.
Let f (x) be the p.m.f. of the r.v. X with a discrete space, S
Let u (X) be a function of X. The expected value is the weighted mean of u (x) where the
weights are defined by f
Variance
STAT 400
September 8, 2016
Definition: Variance. The expected value provides information about the typical value observed
from a distribution and is also referred to as the first moment.
Let denote the expected value.
The second moment is used
Exponential Distribution
STAT 400
February 23, 2017
Example 1 Suppose we are interested in a Poisson process X defined over the unit interval [0, 1]
with as the expected number of events. We are interested in the amount of time, say W , that it
takes for
STAT 400 / MATH 463
Fall 2011
Homework #1
(due Friday, September 2, by 3:00 p.m.)
No credit will be given without supporting work.
1.
Suppose that P ( A ) = 0.60, P ( B ) = 0.40, P ( A
What is the probability that
a)
either A occurs or B occurs (or both)
Normal Distribution
STAT 400
September 29, 2016
Definition The normal distribution, or Gaussian distribution, is one of the most well known pdfs.
If X N (, 2 ) the pdf is,
C
D
1
(x )2
f (x) = exp
, < x <
2 2
2
(1)
E(X) = and V ar(X) = 2
Note that Z N
Confidence Interval for Population Mean
STAT 400
March 31, 2016
Remark: Recall that the CLT implies that if X1 , . . . , Xn are independent with a common finite
mean and variance that,
X
n
D
N (0, 1) , n
(1)
using
If n is large (e.g., n > 30), we ca
Methods of Enumeration
STAT 400
September 1, 2016
Definition: Suppose an experiment, Ei has ni possible outcomes. The composite experiment Ei Ej
has ni nj possible outcomes.
Example 1 Suppose you have 5 shirts (E1 ), 7 pairs of pants (E2 ), and 3 pairs of
Bernoulli Trials
STAT 400
February 8, 2016
Definition: Bernoulli Experiments. Bernoulli trials are random experiments where an outcome is
classified into one of 2 mutually exclusive and exhaustive categories.
A sequence of Bernoulli trials is conducted m
Gamma Distribution
STAT 400
September 27, 2016
Example 1 Suppose we are interested in a Poisson process defined over the unit interval [0, 1]
with as the expected number of events, i.e., X P oisson(). We are interested in the amount
of time, say W , that
Continuous Random Variables
STAT 400
September 22, 2016
Definition: If S is an interval or union of intervals, then X is a continuous-type random variable.
The following properties must hold for f (x) to be a probability density function (p.d.f.)
f (x) >
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November 07, 2016
Ninetyyearsago,RonaldFisherchangedscienceforever.Withhisbook,StatisticalMethodsforResearchers,the
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Confidence Interval for Population Mean
STAT 400
July 15, 2016
Remark: Recall that the CLT implies that if X1 , . . . , Xn are independent with a common finite
mean and variance that,
X
n
D
N (0, 1) , n
(1)
using
If n is large (e.g., n > 30), we can
STAT 400
Spring 2014
Homework #7
(due Friday, March 21, by 3:00 p.m.)
No credit will be given without supporting work.
Several students cleverly and correctly pointed out that problems 3 & 4 on Homework 6 were
somewhat unrealistic, since a Normal distribu
STAT 400
Spring 2014
Name _
Version A
NetID _
Quiz 4
(10 points)
Be sure to show all your work; your partial credit might depend on it.
No credit will be given without supporting work.
1.
Alex purchased a used car at Honest Harrys Used Car Dealership. If
STAT 400
Spring 2014
Name _
Version C
NetID _
Quiz 4
(10 points)
Be sure to show all your work; your partial credit might depend on it.
No credit will be given without supporting work.
1.
The number of deer struck by cars on the highway between Anytown an
STAT 400
Spring 2014
Name _
Version D
NetID _
Quiz 4
(10 points)
Be sure to show all your work; your partial credit might depend on it.
No credit will be given without supporting work.
1.
The number of deer struck by cars on the highway between Anytown an
STAT 400
Spring 2014
Name _
Version B
NetID _
Quiz 4
(10 points)
Be sure to show all your work; your partial credit might depend on it.
No credit will be given without supporting work.
1.
Alex purchased a used car at Honest Harrys Used Car Dealership. If
Lecture Questions
STAT 400, Week 1, Culpepper
1. Two players A and B play a game that requires repeatedly flipping a fair coin. Player A gains
a point if the coin is a head and Player B gains a point if the coin is a tail. Each player
gains a point when t
Lecture Questions
STAT 400, Week 2, Culpepper
1. The family dog is missing after a picnic in the park. Three hypotheses are suggested: = it
has left the park and gone home; = it is still in the park picnic area; = it has wandered off
into the park woods.
Statistical Tests for Population Proportions
STAT 400
November 8, 2016
Example 1 A scientist wishes to test if a new treatment has a better cure rate than the traditional
treatment which cures only 60% of the patients. In order to test whether the new tre
Confidence Interval for Difference in Population
Means
STAT 400
November 1, 2016
Definition (Confidence interval for 1 2 , 12 and 22 known)
Let X1 N (1 , 12 ) and X2 N (2 , 22 ).
Consider two independent random samples of X1 and X2 of X11 , . . . , X1n1
Tests for Variances
STAT 400
November 10, 2016
Remark Sometimes researchers formulate hypotheses about the population variance, 2 .
2
Recall that if X1 , . . . , Xn are distributed N (, 2 ) that (n 1) S2 2 (n 1).
Let 02 be the hypothesized value under H