Stat 653 HW1
Exercise 1.
Divya Nair
Show that V ar(X ) = E (X 2 ) (E (X )2 .
Proof.
V ar(X ) = E [(X E (X )2 ]
= E [X 2 2E (X ) X + (E (X )2 ]
= E (X 2 ) E (2E (X ) X ) + E (E (X )2 )
Since E (X ) is a constant and E (c) = c for any constant c,
V ar(X ) =
Stat 653 HW6 - Agresti
Divya Nair
Exercise (4.1). A study used logistic regression to determine characteristics associated with
cancer patient achieved remission (1
=
Y = whether a
yes). The most important explanatory variable was a labeling index
(LI) th
Stat 653 HW5
Divya Nair
2
2
(2.26). A chi-squared variate with degrees of freedom equal to df has representation Z1 + +Zdf ,
where Z1 , . . . , Zdf are indepdent standard normal variates.
Exercise 1
a. If Z has a standard normal distribution, what distrib
Divya Nair
Stat 653 HW 9
Exercise (6.1). A model t predicting preference for President (Democrat, Republican, Independent) using
x=
annual income (in $10,000 dollars) is
1. State the prediction equation for
log
D
I
R
D
log
= 3.3 0.2x
and
log
R
I
= 1.0 + 0
Stat 653 HW4
Divya Nair
(2.18). Table 2.13 shows data from 2002 General Social Survey cross classifying a person's
perceived happiness with their family income. The table displays the observed and expected cell counts and
the standardized residuals for te
Stat 653 HW8 - Agresti
Divya Nair
(7.1b). For Table 2.1 on X =gender and Y =belief in an afterlife, Table 7.16 shows the results of
tting the independence loglinear model. Report Y . Interpret Y Y .
1
2
j
Exercise
From Table 7.16, Y = 1.4165 and Y = 0. Th
Stat 653 HW3
Divya Nair
Exercise 1 (2.1). An article in the New York Times (February 17, 1999) about the PSA blood test for
detecting prostate cancer stated that, of men who had this disease, the test fails to detect prostate cancer
in
1
in
4
(so called f
Stat 653 HW7 - Agresti
Divya Nair
(2.16). The table below comes from one of the rst studies of the link between lung cancer and
smoking, by Richard Doll and A. Bradford Hill. In 20 hospitals in London, UK, patients admitted with
lung cancer in the previou
STATS 453/653, Fall 2011
Midterm (November 8, 2011)
Name:
Total
(100 pts)
Problem 1. [10 points] Derive the mean of a Binomial random variable with parameters
n and p.
1
Problem 2. A random sample of 200 adults is classied below according to gender and
at
Stat 653 HW2
Exercise 1.
Divya Nair
Find MLE (Maximum Likelihood Estimator) for the following parameters:
1. Probability of success p in Bernoulli(p) model.
Let X be a Bernoulli random variable with parameter p. Let X1 , , Xn be the independent
random sam