Introduction to Econometrics Assignment

Introduction to Econometrics Assignment
Econometrics PS 1
Due: Feb 2
Complete the entire problems in each section as required. There are two sections!
Section 1: Probability theory: Expected Value and Lotteries (ONE QUESTION TOTAL)
We discussed how the sample mean can be skewed by an extreme value. In a sample of 100 people from Texas, if a multi-millionaire oil baron is randomly chosen for the sample, the mean income in the sample would be skewed higher than the median.
The sample mean is sometimes referred to as the expected value, written E[X] for the expected value of X. In probability theory the expected value is the sum of all potential outcomes, weighted by the probability/chance of the occurrence. For example, assume you are close friends with the oil baron. You need money for school, and as your friend he will agrees to give you one of two cars he never drives, which you will immediately sell for cash. He will flip a coin to determine which one, giving you a 50/50 chance of each. Let’s say one car is worth $12,000 and the other car is worth $118,000. The expected value is written E[X] = 0.5 × $12,000 0.5 × $118,000 = $65,000. Notice that this is also the average of the two values.
Question 1: Consider a random lottery, where 2,250 people enter their name (only once per-person) and a machine selects one winner at random. Each player has an equal chance of selection and the winning prize is $425,000.
a. Absent any costs associated with winning or playing the lottery, what is the expected value of entering the lottery one time?
b. Assume the winner must pay a 20% tax on lottery winnings. Further, the dealer wants to charge an entry fee. Exactly 2,250 people believe in luck and will play if the expected value of the gamble is greater than or equal to zero. What is the maximum entry fee the dealer can charge? Will the dealer make a profit?
c. What is the fundamental difference between the typical Powerball or Megamillions lottery and the one we established in our example above? Use two sentences or less to explain.
Section 2: Stata Exercises (FIVE QUESTIONS TOTAL)
For this section you will download data from this site: https://www.stata.com/texts/eacsap/
Connect to the virtual Stata console here: https://vcon.lib.uh.edu/portal/webclient/index.html

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