Solve the following version of the two-finger Morra game (which is equivalent to the penny-matching game in Section 11.1):
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- In Exercises 11 to 18, state the hypothesis and the conclusion of each statement. If you go to the game, then you will have a great time.arrow_forwardAs a generalization of Example 5.3(figure), consider a test of n circuits such that each circuit is acceptable with probability p, independent of the outcome of any other test. Show that the joint PMF of X, the number of acceptable circuits, and Y, the number of acceptable circuits found before observing the first reject, is PX,Y(x,y) = ((n-y-1)C(x-y))*p^(x)*(1-p)^(n-x) For 0 ≤ y ≤ x < n p^(n) For x=y=n 0 otherwise Hint: For 0 ≤ y ≤ x < n, show that {X = x, Y = y} = A ∩ B ∩ C, where A: The first y tests are acceptable. B: Test y + 1 is a rejection. C: The remaining n − y − 1 tests yield x − y acceptable circuitsarrow_forwardA fourth-grade teacher suspects that the time she administers a test, and what sort of snack her students have before the test, affects their performance. To test her theory, she assigns 90 fourth-grade students to one of three groups. One group gets candy (jelly beans) for their 9:55 AM snack. Another group gets a high-protein snack (cheese) for their 9:55 AM snack. The third group does not get a 9:55 AM snack. The teacher also randomly assigns 10 of the students in each snack group to take the test at three different times: 10:00 AM (right after snack), 11:00 AM (an hour after snack), and 12:00 PM (right before lunch). Examining the graph and the table of means, which of the following is a null hypothesis that might be rejected using a two-factor analysis of variance? Check all that apply. There is no interaction between the type of snack and the time of test μ10:00 AM10:00 AM ≠ μ11:00 AM11:00 AM ≠ μ12:00 PM12:00 PM μ10:00 AM10:00 AM = μ11:00 AM11:00 AM =…arrow_forward
- if Z = 3 (a) How many pure strategy profiles exist in this game? (b) In the unique subgame perfect Nash equilibrium, what is the sum of the payoffs to the two players?arrow_forwardConsider a symmetric game with 10 players. Each player chooses among three strategies: x, y, and z. Let nx denote the number of players who choose x, ny denote the number of players who choose y, and nz denote the number of players who choose z. (So, nz = 10−nx−ny.) The payoff to a player from choosing strategy x is 10−nx (note that nx includes this player as well), strategy y is 13−2ny (again ny includes this player as well), and strategy z is 3. (a) Show that a Nash equilibrium must have at least one person choosing x and at least one person choosing y. (Hint: In a Nash equilibrium, no player can do better by doing something different.) b) Find all Nash equilibria.arrow_forwardA casino offers the following game, which costs 10 dollars to play. Two cards are selected at random without replacement from a standard deck of 52 cards. If both of the cards are kings, you win 220 dollars and get your 10 dollars back. If exactly one of the cards is a king, you win 20 dollars and get your 10 dollars back, Otherwise, you lose the 10 dollars. Let X be equal to the amount of money won as the result of playing this game one time, where winning a negative amount is equivalent to losing that amount. Find P(X>0) Find E(X)arrow_forward
- Dogs are inbred for such desirable characteristics as blue eye color; but an unfortunate by-product of such inbreeding can be the emergence of characteristics such as deafness. A 1992 study of Dalmatians (by Strain and others, as reported in The Dalmatians Dilemma) found the following: (i) 31% of all Dalmatians have blue eyes. (ii) 38% of all Dalmatians are deaf. (iii) 42% of blue-eyed Dalmatians are deaf. Based on the results of this study is "having blue eyes" independent of "being deaf"? No, since .31 * .38 is not equal to .42. No, since .38 is not equal to .42. No, since .31 is not equal to .42. Yes, since .31 * .38 is not equal to .42. Yes, since .38 is not equal to .42. Submit QuestionQuestion 13arrow_forwardConsider the following normal form of the game with two players. What is the Nash Equilibrium of this game?arrow_forward9. A research center claims that 24% of adults in a certain country would travel into space on a commercial flight if they could afford it. In a random sample of 700 adults in that country, 28% say that they would travel into space on a commercial flight if they could afford it. At α=0.05, is there enough evidence to reject the research center's claim? Complete parts (a) through (d) below. Question content area bottom Part 1 (a) Identify the claim and state H0 and Ha. Identify the claim in this scenario. Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or a decimal. Do not round.) A. The percentage adults in the country who would travel into space on a commercial flight if they could afford it is not enter your response here %. B. No more than enter your response here % of adults in the country would travel into space on a commercial flight if they could afford it. C. At least…arrow_forward
- 1. Fifty percent of the coffee brewed at a particular coffeeshop will stay fresh for 30 minutes. The owners of the coffeeshop are considering trying a different brand of coffee bean because they have heard that it will keep brewed coffee stay fresh for more than 30 minutes. To check this out, they brew 20 pots of coffee with the new bean and decide that they will conclude that the new bean is better if 15 or more of these pots of coffee still taste fresh after 30 minutes a) What is the probability that the coffeeshop owners will conclude that the new bean is better even if, in fact, it is no better than the beans they have always used in the past? b) In a second test, the coffeeshop owners brew 25 pots of coffee with the new bean and test the same hypotheses as in part 'a' using an alpha of 01. Suppose that the new bean would actually allow 80% of these pots of coffee to stay fresh longer than 30 minutes: what is the power of the coffeeshop owners' experiment?arrow_forward1. I am playing a gambling game. On each play, I have a 10% chance of winning $12, a 30% chance of breaking even (not winning or losing any money), and 60% chance of losing $5. I play this game 300 times. (a) Write down the box model to represent this situation, including the values on the tickets, the number of repeats of each ticket, and how many draws we will make with replacement from the box. (b) The average of this box is ___________ and the SD of the box is ____________. (c) In 300 plays, my net gain (total amount won or lost) has an expected value of $___________, with a standard error of $___________. (d) What is the chance that I come out ahead (have a positive net gain) after the 300 plays? Use the normal approximation to calculate this. ___________%arrow_forwardConsider a modified version of the board game RISK in which player A is attacking player B. At the beginning of each turn, player A rolls N 4-sided dice where N+1 is the number of armies that player A has (So if A has 3 armies, A starts by rolling 2 4-sided dice). Player B always rolls a single 6-sided die. If the biggest roll among the dice that A rolls is bigger than player B's roll, then player B loses an army. If all of player A's rolls are less than player B's roll, then player A loses an army. If it is a tie, neither player loses an army. The rolls are repeated until either B has no armies (A has captured the territory) or A has only one army (the attack has been repelled). If A has two armies and B has one army find the probability for each event: A loses an army, B loses an army and neither lose an army If A has three armies and B has one army find the find the probability for each event: A loses an army, B loses an army and neither lose an army If A has three armies and…arrow_forward
- Elementary Geometry For College Students, 7eGeometryISBN:9781337614085Author:Alexander, Daniel C.; Koeberlein, Geralyn M.Publisher:Cengage,