Find a) the method of moments estimate of theta, b) the m.l.e of theta, and c) the
asymptotic variance of the mle, for the following distributions: I. X1,X2,.,Xn is an iid
sample from a Rayleigh distribution with parameter theta > 0, f(x|theta) =
(x/theta
SOLUTIONS: 4.1 Probability Distributions and 4.2 Binomial Distributions
1. The following table contains a probability distribution for a random variable X.
x
P (x)
1
0.16
2
0.22
3
0.28
4
0.20
5
0.14
a. Find the expected value (mean) of X.
x
1
2
3
4
5
P (x
Lecture 4 : The Binomial Distribution
Jonathan Marchini
October 25, 2004
1
Introduction
In Lecture 3 we saw that we need to study probability so that we can calculate the
chance that our sample leads us to the wrong conclusion about the population.
To do
The Binomial Distribution
A. It would be very tedious if, every time we had a slightly different problem, we had to determine the probability distributions from scratch. Luckily, there are enough similarities between certain types, or families, of experim
Christopher Knapp
Probability and Statistics (Fall 2011)
Assignment 2
Problem 1.3.3: A coin is tossed until H is reached. Let the probability set function P assign
1
to the space C =fT 0 H; T 1 H; T 2 H; : : :g to the values P (T n H) = ( 2 )n+1 for each
Economics 203a
Homework # 3
Anton Cheremukhin
October 23, 2005
5
Exercise 1 If the moment generating function of a random variable X is 1 + 2 et , nd Pr (X = 2 or 3)
3
3
P
n
Proof. (1 p + pet ) = y n py (1 p)ny , hence n = 5, p = 2/3
y
52
40
= 243
Pr(X =
4/28/13 estimation - Why is sample standard deviation a biased estimator of $\sig ma$? - Cross Validated
Cross Validated is a question and answer site for statisticians, data analysts, data miners and data visualization [j x
experts. It's 100% free, no re
APPENDIX C.7
C.7
Binomial Distributions
A55
Binomial Distributions
Find probabilities for binomial experiments.
Find binomial distributions.
Approximate binomial distributions for experiments with large numbers
of trials.
Binomial Experiments
A binomia