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September 29, 2005
The Poisson Distribution
The Poisson distribution approximates the binomial distribution for a large n and a small p.
Note that the right-hand column above and the left-hand column below are the same.
Posted by bparke at 09:58 PM | Comments (0)
Problems
Posted by bparke at 09:56 PM | Comments (0)
September 27, 2005
The Binomial Distribution
Posted by bparke at 09:39 PM | Comments (0)
Homework Problems
Posted by bparke at 10:46 AM | Comments (0)
September 22, 2005
The Number of Aces in a Five Card Hand
The classic application of the committee problem is the Hypergeometric Distribution. This is a general formulation of the distribution of the random variable that is the number of aces in a five card hand.
Posted by bparke at 10:19 PM | Comments (0)
Combinations and Permutations
We studied a handout that lists all 120 possible committees of 2 people chosen from a group of 5 people.
The handout "proves" the following results.
Posted by bparke at 10:15 PM | Comments (0)
September 20, 2005
The Space Shuttle Problem
The video projector failed so we filled in with the Space Shuttle Problem. You have three components. Each has an 80% chance of working. What is the probability all three components work?
There are some hard ways to solve this problem, and there is the easy way. Hint: think one minus.
Posted by bparke at 10:10 PM | Comments (0)
n vs. n-1
We tried to understand the mysteries of n vs. n-1.
We divide by n-1 when we calculate the sample variance because that produces an "unbiased" estimate of the population variance.
In calculating the sample variance, one "degree of freedom" is used up calculating the sample mean. This is "obvious" if you consider a sample of two numbers. One degree of freedom is the sample mean, and the other degree of freedom is how far each number is from the mean, which is precisely in the middle.
Posted by bparke at 10:05 PM | Comments (0)
Bayesian Inference
The textbook for this course takes the point of view of Classical Statistical Inference. There is an alternative that we can mention briefly, Bayesian Inference. If you look closely, you will see that people are Bayesians in their approach to life, where holding a subjective prior is not a problem.
Suppose A is observable, but we are really interested in B, which in more complex applications is an unknown parameter. Bayes' Theorem translates information on the probability of A given B into a statement about the probability of B given A.
We can then talk about the prior (unconditional) probablity of B and the posterior (conditional on A) probability of B.
Posted by bparke at 09:51 PM | Comments (0)
September 15, 2005
Counting
The classic "committee problem" can be stated as: how many ways are there to choose a committee with x members from a group of n people?
Posted by bparke at 09:30 PM | Comments (0)
Tables, Trees, Venn Diagrams
For many basic probability problems, the most important step is making a good choice among the possible approaches: list the sample space, formulas, Venn diagram, table, tree, think hard.
Today's example and a couple of formulas:
A Venn diagram (the instructor's favorite):
A Venn diagram can handle three events. Four or more is in general impossible.
Do you prefer a table?
Or a tree?
3.26 provides an illustration of the point that there are multiple ways to arrange Venn diagrams (and trees and tables) for a given problem.
Posted by bparke at 09:17 PM | Comments (0)
September 13, 2005
Probability
We started with the definition of "round."
We moved on to the definition of "probability."
This is pretty deep so we will proceed with examples.
Here's one:
The definition of "fair coin" or "fair dice" is intertwinced with the definition of probability.
There are lots of new concepts to define once you get into this probability stuff.
One more example:
Reading the textbook might help.
We will spend the next few lectures going over this material when we talk about probability distributions.
Posted by bparke at 09:07 PM | Comments (0)
September 08, 2005
Multivariate Descriptive Statistics
Posted by bparke at 10:03 PM | Comments (0)
September 07, 2005
Stata Movies
Link for help getting started with Stata. (Scroll down past homework assignments.)
Posted by bparke at 09:45 PM | Comments (0)
September 06, 2005
Descriptive Statistics
Posted by bparke at 10:00 PM | Comments (0)
September 01, 2005
Introduction
Posted by bparke at 09:53 PM | Comments (0)