#
# TULIKA THAKUR (STUDENT ID: 001100980)
DATE: 02/10/2016
# R Script: ST502Homework4
Spring2016
#
# 1 A) Estimate the standard error of both method of moments estimators using
a parametric bootstrap.
y_bar < 11.3
sB_sq < 6.41
n < 30
N < 10000
mu_ha
ST 502  Homework 2
7.2
7.4
7.11
Other Problems:
1. Suppose that E() = a + b.
e
(a) Construct an unbiased estimator of .
(b) Express the MSE of your unbiased estimator as a function of V ar().
e
(c) Give an example of a value of b for which the MSE of you
ST 502  Problem Session 2
7.1
7.3
7.5
7.6
7.10
Other Problems:
1. If Bias() = 5, what is the expected value of the estimator?
e
2. Suppose that 1 and 2 are unbiased estimators of and their variances are given by
e
e
12 and 22 , respectively. Consider the
ST 502  Homework 5
8.4e
8.16d
8.21c  Also, explain why sufficient statistics are useful.
8.62  You can either sketch the plots by hand or print them out and include them (no need
to submit R code)
8.66
8.72
Other Problems:
1. Suppose Yi iid U (0, ).
(a
ST 502  Homework 4
8.2  also create a 95% CI for
8.7a
8.13  also create a 99% CI for
0
8.18ab  For part b, your answer will be in terms of ()
8.52b
R Problem: For the R part that follows, you should create an R script that you will save
and upload t
ST 502  Problem Session 1
1. Let X1 , X2 , . be a sequence of independent RVs with E(Xi ) = i and V ar(Xi ) = i2 .
P
P
p
.
Further, suppose n12 ni=1 i2 0 and n1 ni=1 i as n . Show that X
2. Suppose that Y N (, 2 ).
(a) Use MGFs to find the distribution o
ST 502  Homework 3
7.9  When actually calculating the interval, ignore the fpc.
7.14
7.17
7.20
7.22
Other Problems:
R Problems: For the R parts that follows, you should create an R script that you will save
and upload to moodle. Your R file should adher
ST 502  HW 1
1. Define the term RV and distribution.
2. For a continuous bivariate random vector (X, Y ), prove that E(ag1 (X, Y )+bg2 (X, Y )+
c) = aE(g1 (X, Y ) + bE(g2 (X, Y ) + c.
3. Let X1 , X2 , . be a sequencePof independent random variables with
ST 502  Homework 7
9.1
9.4c
9.9
9.19 Note: Part b) The form of the LRT is to Reject H0 for =
9.30
2
3x
< c or x > (2/3)c = c2 .
Other Problems:
1. Let X1 , , Xn be a random sample from the exponential distribution with pdf an
exp(1/)
1
fX (x) = ex/ , 0 <
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#
# TULIKA THAKUR (STUDENT ID: 001100980)
DATE: 02/17/2016
# R Script: ST502Homework5
Spring2016
#
# Part(a)
# Given values of mu and sigma_square.
mu < 3
variance < 4
# Generate a sample of size 5 from the known distr.
n < 5
y < rnorm(n, mean=mu, s
ST 502 Notes
Important points from ST 501
Goal: Make inference about a population parameter using a sample.
if Y1 , ., Yn are independent and identically dis
We have a
tributed.
 a function of RVs from a random sample.
Distribution of a statistic called