Let's say David bought a lottery ticket that costs 1,000 dollars.
The ticket can be sold a total of 4,000million tickets. However, some tickets were unsold, so 3,987,284,836 tickets were sold in total.
The prize money is a random variable, X and has five different random variables following: 0 dollars, 1,000 dollars, 5,000 dollars, 10,000dollars, 20,000,000 dollars, 500,000,000 dollars.
So the questions are: Make sure to use formulas and show all of your calculation processes.
1. Using the amount of winning tickets that were printed and distributed, create your own probability table and compare with the one that is provided at the back of the ticket. Use four decimal digits to fill your table. Make sure you have probability distribution. Otherwise, calculating expectation would not make sense.
2. What is the probability to lose the game? In other words, P(X=0)?
3. What is the probability to win the game? In other words, P(X taking nonzero value)?
4. Using the table you created in problem number 4, calculate the expected value of X.
5. Calculate the variance of X.
6. Calculate expectation of Y where Y=X-c and c is the ticket price you found in problem number 1.
7. Calculate the variance of Y.
