Signature Assignment Important Instructions to the Student: 1. All explanations must be typed. The supporting math work must be neat and suitable for copying or scanning to insert into this document. The final document should be saved and submitted as a single .pdf, .doc, or .rtffile. 2. Submit your assignment via Blackboard by the deadline established by your instructor. A charity organization hosts a raffle drawing at a fund raising event. The organization sells 2500 tickets at a price of $8 each. Winning tickets are randomly selected, with 30 prizes of $100, 10 prizes of $500, and 1 grand prize of $8000. Suppose you buy one ticket. Let the random variable X represent your net gain from playing the game once (remember that the net gain should include the cost of the ticket). 1. Use the table below to help you construct a probability distribution for all of the possible values of X and their probabilities. X (Net Gain) Probability 2. Find the mean/expected value of X. (Round to two decimal places.) 3. In complete sentences, describe the interpretation of what your value from #2 represents in the context of the raffle. 4. If you were to play in such a raffle 100 times, what is the expected net gain? 5. Would you choose to buy a ticket for the raffle? (Your response should be a short paragraph, written in complete sentences, to explain why or why not.) 6. What ticket price would make it a fair game, so that, on average, neither the players nor the organizers of the raffle win or lose money? (Round to two decimal places.) 7. If you were organizing a raffle like this, how would you change the game (ticket prices, number of tickets, prize amounts, etc.) in order to encourage more people to purchase tickets while still raising at least $4000 for your organization? Your response should include a short paragraph, written in complete sentences, with an explanation of the specific adjustments or changes that you would make and how these changes would encourage more people to purchase tickets. 8. Construct a new probability distribution describing the net gain (from the player's perspective) for the game with your proposed changes from #7