Interval Estimation Section 11.1-11.2
) varies from
The interval (
sample to sample.
For a given random sample, the
) , i.e., the
We now understand (Chapter 10) how to find point
estimators of an unknown param
General Methods for Obtaining Estimators
Data: Random Sample from a Population of interest
o Real valued measurements:
o Assumption (Hopefully Reasonable)
o Model: Specified Probability Distribution
f (x | )
Section 11.5 Estimation of difference of two proportions
As seen in estimation of difference of two means for nonnormal population based on large sample sizes, one can use
CLT in the approximation of the distribution of sample mean.
Therefore, an approxim
Statistics 421: Homework #1. Solution
From the result of Exercise 8.22,
24 we already know that by CLT, as n
Z N (0, 1)
since Xi 21 , i = 1, , n implies
Week 12 | Distributions of functions of random variables I
Textbook sections: 7.27.4, 6.4.
Distribution function technique, change-of-variable (transformation) technique.
General strategy (X Y ): Let X be a random variable with pdf (or pmf) fX o
Week 11 | Moments of multivariate distributions
Textbook sections: 4.64.8
Product moments, linear combinations of random variables, conditional expectations.
11.1. Read textbook example 4.15. Suppose that the discrete random variables
Week 8 | Special distributions: The binomial models
Textbook sections: 5.15.5, 5.8, (5.6, 5.9).
Bernoulli trials, binomial, geometric, negative binomial distributions, multinomial distributions.
8.1. Find the mean of the random variabl
Week 10 | Special distributions: The normal and related distributions
Textbook sections: 6.56.7
Normal and bivariate normal distributions.
10.1. Read textbook examples 6.26.4, and evaluate the following quantities.
(a) For Z N (0, 1);
Week 7 | Some special expectations & Midterm exam
Textbook sections: 4.5
Moment generating function, cumulant generating function.
Taylor series: Let f be a smooth function on some interval I R.
The Taylor series for f at a I is
f (x) = f (a) +
Section 11.3 Estimation of the Difference of Two population means
I Example: Two different manufacturers of long life bulbs:
0 Life times are Normal with (unknown) means ,ui, i = 1,2
andvan'ances of 2250005 23600.
0 Want to estimate the difference in thei
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Week 3 | Bayes Theorem and random variables
Textbook sections: 2.6-2.8, 3.1-3.2
The law of total probability, Bayes theorem, random variable and its distribution.
More tips for computing probabilities: Suppose we have a (random) sequence consist
Week 9 | Special distributions: The Poisson and related models
Textbook sections: 5.7, 6.26.3
Poisson, gamma, exponential and chi-square distributions
9.1. Let X Binomial(n, /n) for some > 0 and a large natural number n.
(a) By using t