Four apples and four oranges are distributed between two boxes in such a way that each of them has four fruits. At each step, we withdraw one fruit from each box and exchange them. Let Xn be the number of apples in the first box. Give the transition probability matrix for Xn. Find long run proportion which is to find Pi1,Pi2,Pi3,Pi4.
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Four apples and four oranges are distributed between two boxes in such a way that each of them has four fruits. At each step, we withdraw one fruit from each box and exchange them. Let Xn be the number of apples in the first box. Give the transition probability matrix for Xn. Find long run proportion which is to find Pi1,Pi2,Pi3,Pi4.
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- Let X1, X2, X3, X4 have the joint probability density functionf(x1, x2, x3, x4) = (24e−(x1+x2+x3+x4), 0 < x1, x2, x3, x4 < ∞0, elsewhereLet Y1 = X1, Y2 = X2 − X1, Y3 = X3 − X2, Y4 = X4 − X3.(i) Using the change of variable technique, find the joint probability density functionof Y1, Y2, Y3, Y4(ii) Find the conditional distribution of Y4 given Y1, Y2, Y3Please do not give solution in image format thanku Two Manufacturers supply food to a large cafeteria. Manufacturer A supplies 40% of the soup served in the cafeteria, while Manufacturer B supplies 60% of the soup that is served. 3% of the soup cans provided by Manufacturer A are found to be dented, while 1% of the cans provided by Manufacturer B are found to be dented. Given that a can of soup is dented, find the probability that it came from Manufacturer B.n people guess an integer between 1 and 100, and the winner is the player whose guess is closest to the mean of the guesses + 1 (ties broken randomly). Which of the following is an equilibrium: a) All announce 1. b) All announce 50. c) All announce 75. d) All announce 100
- Using the random variables X and Y from Table 2.2, consider two new random variables W = 4 + 8X and V = 11 - 2Y. Compute (a) E(W) and E(V); (b) J2W and J2V; and (c) JWV and corr(W, V).A factory production process produces a small number of defective parts in its daily production. Is the number of defective parts a discrete or continuous random variable?Halsen, a marketing manager at Business X, has determined four possible strategies (X1, X2, X3, and X4) for promoting the Product X in London. She also knows that major competitor Product Y has 4 competitive actions (Y1, Y2, Y3 and Y4) it’s using to promote its product in London, too. Ms. Halsen has no previous knowledge that would allow her to determine probabilities of success of any of the four strategies. She formulates the matrix below to show the various Business X strategies and the resulting profit, depending on the competitive action used by Business Y. Determine which strategy Ms. Halsen should select using. Maximax, maximin or minimax regret? Business X Strategy Business Y Strategy Y1 Y2 Y3 Y4 X1 25 57 21 26 X2 17 29 20 34 X3 47 31 32 37 X4 35 27 30 35
- Halsen, a marketing manager at Business X, has determined four possible strategies (X1, X2, X3, and X4) for promoting the Product X in London. She also knows that major competitor Product Y has 4 competitive actions (Y1, Y2, Y3 and Y4) it’s using to promote its product in London, too. Ms. Halsen has no previous knowledge that would allow her to determine probabilities of success of any of the four strategies. She formulates the matrix below to show the various Business X strategies and the resulting profit, depending on the competitive action used by Business Y. Determine which strategy Ms. Halsen should select using, the following decision criteria. Please explain your answer for each strategy. a)Maximax; b)Maximin; c)Minimax regret Business X Strategy Business Y Strategy Y1 Y2 Y3 Y4 X1 25 57 21 26 X2 17 29 20 34 X3 47 31 32 37 X4 35 27 30 35In a Godiva shop, 40% of the cookies are plain truffles, 20% are black truffles, 10% are cherry cookies, and 30% are a mix of all the others. Suppose you pick one at random from a prepacked bag that reflects this composition. a. What is the probability of picking a plain truffle? b. What is the probability of picking truffle of any kind? c. If you instead pick three cookies in a row, what is the probability that all three are black truffles?You are modeling a qualitative variable that takes on two classes (classes 1 and 2). In trying to classify observation 11 (out of 20) you compute the conditional probability for class 1 as 0.51. How would you classify this observation?
- Applied Machines produces large test equipment for integrated circuits. The machines are made to order, so the production rate varies from month to month. Before shipping, each machine is subject to extensive testing. Based on the tests the machine is either passed or sent back for rework. During the past 20 months the firm has had to rework the following numbers of machines: (given) Consider the example of Applied Machines presented above. Based on the estimate of the probability that a machine is sent back for rework computed from the 20 months of data, determine the following:a. If the company produces 35 machines in one particular month, how many, on average, require rework?b. Out of 100 machines produced, what is the probability that more than 20 percent of them require rework? (Use the normal approximation to the binomial for your calculations).Static Bayesian Games] We consider a games with 2 players. Player 1 has only asingle type; however, Player 2 can have two types I and D, each with probability 50%. Bothplayers have two actions available to them. The game has the following payoffs (P1 is the rowplayer, P2 the column player):For a group of 300 cars the numbers, classified by colour and country of manufacture, are shown in the Black Silver White Korea 33 34 35 Japan 23 9 24 America 16 25 34 Germany 19 16 32 One car is selected at random from this group. Find the probability that the selected car is a black or white car manufactured in Korea.