Question

A theater group holds a fund-raiser. It sells 100 raffle tickets for $6 apiece. Suppose you purchase four tickets. The prize is two passes to a Broadway show, worth a total of $150. Part (a) What are you interested in here? 1.the type of fund-raiser 2.the price of the raffle tickets 3.the total number of raffle tickets sold 4.the amount of winnings Part (b) In words, define the Random Variable X. 1.the number of passes to the Broadway show 2.the amount of winnings 3.the amount of money made selling raffle tickets 4.the total number of raffle tickets sold Part (c) List the values that X may take on. 1. 0, 1, 2, ..., 100 2. −24, 126 3. 1, 2, 3, 4 4. 6, 126 Part (d) Construct a PDF. (Round your answers to two decimal places.)

Answer 1

The student is interested in the amount of winnings in a fund-raiser where raffle tickets are sold. The random variable X represents the amount of winnings, and it can take on values of -24 and 126. The probability density function (PDF) can be constructed based on the probabilities of each value occurring.

Step-by-step explanation:

In this question, the student is interested in different aspects of a fund-raiser. Part (a) asks what the student is interested in, and the correct answer is 4. the amount of winnings. Part (b) asks to define the random variable X, and the correct answer is 2. the amount of winnings. Part (c) asks for the values that X may take on, and the correct answer is 2. −24, 126. Lastly, part (d) asks to construct a PDF, which is a probability density function. To construct this, we need to determine the probability of each value of X occurring. Since the prize is worth $150, the probability of winning $150 is 1/100. The probability of winning nothing is 99/100. Therefore, the PDF is: X=-24 with probability 99/100 and X=126 with probability 1/100.