7.55 The amounts of electricity bills for all households in a city have a skewed probability distribution with a
mean of $140 and a standard deviation of $30. Find the probability that the mean amount of electric bills for a
random sample of 75
Homework 8 - due Thursday , March 27
5.52Which of the following are binomial experiments? Explain why.
a. Drawing 3 balls with replacement from a box that contains 10 balls, 6 of which are red and 4 are blue, and
observing the colors of the drawn balls
8.28A consumer agency that proposes that lawyers' rates are too high wanted to estimate the mean hourly rate for
all lawyers in New York City. A sample of 70 lawyers taken from New York City showed that the mean hourly
rate charged by them is
Part I bivariate data
Problem 1 (SSxx =Sxx, SSyy=Syy, SSxy=Sxy different notation )
Problem 3 The following table gives the temperatures(X) (in degrees Fahrenheit) at 6 P.M. and the attendance (Y)
(rounded to hundreds) at a minor leag
A marketing analyst is studying the relationship between 3;: money" spent on television advertisement.
and y: iiierease in sales, One study reported the data in the Figure below for a particular company.
Data are in thousands of dollars.
Homework6: Visualize the CLT through simulation and
Agenda: Make R application with Shiny
The Central Limit Theory (CLT) states that if X1 , X2 , . . ., Xm are iid random variables that follow a
= 1 P Xi has an approximate
1. suppose one has the set of n data points, cfw_(xi , Yi = yi ) for i = 1, . . . , n, and one wishes to fit the
model E(Yi | xi ) = 0 + 1 xi to n data points. Here, Y1 , . . . , Yn are independent r.v. If 0 and 1 are
estimators of 0 and 1 , Y = 0 + 1 x i
1. 9.58, 9.59, 9.80, 9.82, 9.83
2. It is known that the probability p of tossing heads on an unbalanced coin is either 1/4 or 3/4. The
coin is tossed twice and a value for Y , the number of heads, is observed.
(a) What are the possible values of Y ?
Functions as Objects
author: date: 4 November 2015 font-family: Garamond transition: none
Writing our own functions
Dividng labor with multiple functions
Refactoring to create higher-level operations
Using apply, sapply, ddply etc., to avoid it
1. We are interested in testing whether or not a coin is balanced based on the number of heads Y on 36
tosses of the coin. (H0 : p = .5 versus Ha : p 6= .5). If we use the rejection region |y 18| 4, what is
a. the value of ?
b. the value of if p = .7?
STAT 597A- Spring 2017
Lab: Monte Carlo Simulation-Importance Sampling
Simulation methods are particularly well suited to estimating means of random variables. If
we can simulate many random variables with the appropriate distribution, we
R b can average
Homework 7: Likelihoods
When we have independent samples \(x_1, x_2, . . . x_n\) from a common probability density \(p(x),\) the
joint probability density of the whole sample is \[ \prod_cfw_i=1^np(x_i). \] When we are not sure what the
right density \(p\
Homework 5: split-apply-combine!
A dataset bnames.csv is at http:/people.math.umass.edu/~wei/Teaching/STAT597_Spring17/bnames.csv.
It contains the 1000 most popular male and female baby names in the US, from 1880 to 2008. There
are 258,000 records (
By Tatiana Filipovich
A late employee can cause an effect to productivity in
Late employees, especially those who come in late
often, impact multiple areas of the business, including
Organizing and graphing data.
Graphing data is the first and often most
important step in data analysis
The following handout discuss common graphs
for qualitative and quantitative variables.
In 1969 the war in Vietnam was at its he
More Data Structures
author: STAT597A date: Jan, 2017 font-family: Garamond
Structures of structures
Vector structures, starting with arrays
Many data structures in R are made by adding bells and whistles to vectors
Stat597A Homework 1 Due Tuesday, Feb 7th, 2017
Your homework must be submitted in with two files: 1. R Markdown format file; 2. a pdf or html file. We
will not (indeed, cannot) grade homeworks in other formats. Your responses must be suppor
Basics of Data
author: STAT597A date: Jan, 2017
The R Console
Basic interaction with R is by typing in the console, a.k.a. terminal or command-line
You type in commands, R gives back answers (or errors)
Menus and other graphical interfaces are extras buil
1. Y is a random variable. Y (1, 1). The pdf is p(y) = ky 2 for some
(a) Find k.
(b) Plot the pdf.
(c) Let Z = Y . Find the pdf of Z. Plot it.
2. U is a random variable on the interval [0, 1]; p(u) = 1.
(a) V = U 2 . On what interval does V l
Stat597A Homework 2 Due Tuesday, Feb 14 before
class through moodle
Your homework must be submitted in moodle with two files: 1. R Markdown format file; 2. a pdf or html
file. We will not (indeed, cannot) grade homeworks in other formats. Your responses m
[Sol] By = 4 degrees of freedom(the value of the parameter in 2 ), we can write
2.05 ) = .90
P (.710721 X 9.48773) = .90
) = .90.
P (2.95 2
Hence the interval ( 9.48773
) forms a 90% confidence interval
1. 8.39, 8.40, 8.58
2. Suppose that Y is normally distributed with mean 0 and unknown variance 2 . Then Y 2 / 2 has a 2
distribution with 1 df. Use the pivotal quantity Y 2 / 2 to find a
(a) 95% confidence interval for 2 .
(b) 95% upper confidence limit f
Stat597A Homework 4
For this homework, we will look trends in baseball team payrolls between the years 1985 and 2010.
The data come from the Baseball Databank http:/baseball-databank.org and is based in part on
Lahmans Baseball Database. Information on th
Stat597A: Lab 2, Feb 1 2017
Things That Go Vroom
Todays agenda: Manipulating data frames; practicing iteration; practicing re-writing code; checking how
reliable random methods are.
General instructions for labs: Please give the commands to answer each qu
Lab 3: Functions
Agenda: Writing functions to automate repetitive tasks; fitting statistical models by method of moments
The gamma distributions are a family of probability distributions defined by the density functions,
f (x) =