ST231: Statistical Inference, Semester 1, 2015
Assignment 2- Due on 12/5/15
Total: 40 marks
Show all working
QUESTION 1
Let X1 , X 2 ,
[10 marks]
, X n denote a random sample from the probability density function
f ( x | ) ( 1) x
0 x 1; 1.
(a)
Find an est

ST231: STATISTICAL INFERENCE, SEMESTER 1, 2015
TUTORIAL 4 (WEEK 9)
1. Let X1 , X 2 , X 3 ,
, X n denote a random sample from the probability density function
f ( x | ) ( 1) x
A.
B.
0 x 1; 1.
Find an estimator for by method of moments and method of maximum

ST231: STATISTICAL INFERENCE, SEMESTER 1, 2015
TUTORIAL 3 (WEEK 6)
1. A random sample of size 25 is drawn from a normal population having mean of 76 and a
standard deviation of 6. A second random sample of size 30 is drawn from a normal population
having

ST231: Lecture 2 (Week 8)
Mr. Dinesh Rao
2
2
Large-Sample Confidence Intervals for ( ) when 1 and 2 are known
1
2
Theorem: If x and x2 are the means of two independent random samples of size
1
2
2
n1 and n2 from populations with known variances 1 and 2 ,

ST231: Lecture 2 (Week 5)
Mr. Dinesh Rao
PROPERTIES OF POINT ESTIMATORS
SUFFICIENCY
Up till now, we have chosen estimators on the basis of intuition. Thus, we
chose X and S 2 as the estimators of and 2 , respectively of the normal
distribution. We have se

ST231: Lecture 4 (Week 8)
Mr. Dinesh Rao
We have discussed the confidence interval for a population mean, difference of two population
mean, population variance and ratio of two population variance. Now we will discuss the
confidence interval for another

ST231: Lecture 2 (Week 7)
Mr. Dinesh Rao
THE METHOD OF MAXIMUM LIKELIHOOD
Previously we looked at method of moments which is easy to use but does not lead to the
efficient estimators. Now we present the method of maximum likelihood that often leads to
MVU

ST231: Lecture 3 (Week 8)
Mr. Dinesh Rao
Confidence Intervals for 2 :
Theorem: If S 2 is the variance of a random sample of size n from a normal
population, a 1 100% confidence interval for 2 is
n 1 S 2 2 n 1 S 2
2
2
where and 2
1
areas
2
2
1
2
2
are

ST231: Lecture 1 (Week 5)
Mr. Dinesh Rao
PROPERTIES OF POINT ESTIMATORS
INTRODUCTION
In the previous section we presented some intuitive estimators for parameters often
of interest in practical problems. An estimator for a target parameter is a
function o

ST231: Lecture 1 (Week 7)
Mr. Dinesh Rao
In this section we will discuss two useful methods for deriving estimators: the method of
moments and the method of maximum likelihood.
THE METHOD OF MOMENTS
In this section, we will discuss one of the oldest metho