Froeb rule of "look ahead and reason back." Can, and how does, the entrant succeed? Is the incumbent ever in control of this game? You may wish to review the old game known as Duopoly, as well as Antoine-Augustin Cournot

If you were charged $8.00 to play this game, you would on average see a ..... (lose/gain) of ...... per spin.

At a back-to-school party, one of your friends lets you play a two-stage game where you pay $3 to play. The game works as follows: flip a fair coin, noting the side showing, and roll a fair standard 4-sided die (numbered 1–4), noting the number showing. If the die shows a 3 and the coin shows tails, then you win $22. If the coin shows heads and the die shows an even number, then you win $9. Otherwise, you do not win anything. Let X be your net winnings. (a) Create a probability distribution for X. Enter the possible values of X in ascending order from left to right. All probabilities should be exact. X       P(X)       (b) Compute your expected net winnings for the game. Round your answer to the nearest cent.

Answer the following question. In a recent competition, each of three teams played each other team once. The results are given in the table below. What was the score of the A vs. C game? Give A's goals first. Team A B C Wins 1 1 0 Losses Ties 0 1 0 1 2 0 Goals For Goals Against 6 3 2 4 2 5 (Remember: Your solution must show appropriate work or reasoning.)

2. You play a game in which 40% of the time you win $3 and 40% of the time you lose $5 and 20% of the time you win $1. Please show your work.

A report just came out that stated that 23.8% of all Americans say that vanilla is their favorite ice cream, 20.9% say that chocolate is their favorite, 9.1% favor butter pecan, 8.2% favor strawberry, and the rest have other favorites. An ice cream shop owner thinks that her customers are not like the rest of America. The table below shows the results of $55 of her patrons' ice cream selections. What can be concluded at the a = 0.05 significance level? a. Complete the table by filling in the expected frequencies. Round your answers to the nearest whole number. Frequencies of Favorite Ice Cream Outcome Frequency Expected Frequency vanilla 216 Chocolate 195 Butter Pecan91 Strawberry 92 Other 361 b. What is the correct statistical test to use? Select an answer V c. What are the null and alternative hypotheses? Но: O The distribution of favorite ice cream for customers at her shop is the same as it is for Americans in general. O The distribution of favorite ice cream for customers at her…