This lecture is in answer to the complaint by Peter Kennedy in his Guide to Econometrics which states that even after a full course on econometrics, students do not understand the most central and fundamental concepts of What is a "Distribution". This lecture is designed to explain the concepts of random variables and their distributions in an intuitive and conceptual way.
This explanation builds on ideas from previous lecture on "Models and Reality", which should be reviewed before watching this lecture.
To access restricted reference materials for this course, including Peter Kennedy's Guide to Econometrics you must first join AZ Research Group. Then follow the link to: IIIE Library
HOMEWORK:
On Friday, I have been asked to go to a two day conference on planning for the new university to be built in PM House. Accordingly, I will not be able to give lecture on Friday. However, I would like the students to watch the following lectures -- just more background material -- instead. There are about four video lecture, so they should do one lecture each day Today, Friday, Saturday, Sunday,
1. Review the material on Models and Reality (which was referred to during the lecture)
https://sites.google.com/site/i2sia2ps/l01/models-versus-reality
2. View the following lectures on this same topic: both available from page AM20: Methodology -- AM20a and AM20b -- are two parts of this video lecture
3. Watch video lecture on: Methodological Mistakes and Econometric Consequences
4, Watch the Urdu lecture -- simple explanation of Normal Distribution --
After all of this preparation, students may want to go through the recording of the Wednesday lecture once again, which is available from
https://sites.google.com/site/i2sia2ps/l7-concluding-remarks/1-distributions-iid
One question that I would like to ask regarding the last lecture (above) - We were trying to solve a problem, but could not. I would like for them to work out the answer and submit
Suppose we generate N iid random variables from a Uniform distribution (-2,+2) and also N iid from a Standard Normal N(0,1)
U(1),...., U(N) is the iid Uniform sample and X(1),...,X(N) is the Normal sample but we do not know which is which.
Now we COUNT the number of variables which are below -1 -- there will be around 25% of them in the interval (-2,-1) for the uniform and 13.8% of the in the interval from (-infinity, -1) in the normal. What is the probabilty that the number of U(,) which falls within this interval is MORE than the number of X(i) which falls within this interval? This is the method we will use to decide which of the two samples is uniform. So this probability is the probability that we will make a CORRECT decision when following this rule. This probability VARIES with N. I would like students to figure out how to calculate this probability for N=20,40,60,80, and 100. And show that the probability increases with N.
Intuitive Explanation of Random Variables & their Distributions — YouTube Video -- 85m
Understanding the Normal Distribution (urdu) — 82m YouTube Video Lecture in Urdu