Show that if a zero-sum game has a saddle point in every 22 submatrix, then it has a saddle point.
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A: Step 1: Calculate Option 1 (Simple Interest)The formula for simple interest is:Simple…
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Q: 7. Let E(x, y) be a two-variable predicate meaning "x likes to eat y", where the domain of x is…
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Q: 13.4. Let f(z) =y-x-3ir² and y be given by the line segment z = 0 to z 1+i. Evaluate. L f(z)dz.
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A: Step 1: Laplace Transform of the SystemLet X(t)=[x(t)y(t)]. Taking the Laplace transform on both…
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Q: 5.10. Discuss the continuity of the function f(z) = at the points 1, -1, i, and -i. 之一 21 3, |2 = 1
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Q: Let W be the subspace spanned by the given vectors. Find a basis for W. 1 0 -1 1 W1 = W2 = 8 -7 ↓1
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- If you played the game in Exercise 1 many times, then you would expect your average payoff per game lo be about $ ____________.Consider a two-player game that is set up with two piles of stones. The two players are taking turns removing stones from one of the two piles. In each turn, a player must choose a pile and remove one stone or two stones from it. The player who removes the last stone (making both piles empty) wins the game. Show that if the two piles contain the same number n ∈ Z+ of stones initially, then the second player can always guarantee a win.If ExxonMobil invests in Venezuela's oil fields, it runs the risk that Venezuela will later partially nationalize the assets. The payoffs are represented in the game tree illustrated in the figure to the right Nationalize (24,96) Suppose that the parties could initially agree to a binding contract that Venezuela would pay ExxonMobil x dollars if it nationalizes the oil fields. How large does x have to be for ExxonMobil to invest in Venezuela? Government Venezuela (60,60) Don't nationalize ExxonMobil The value of x would have to be at least equal to $ for ExxonMobil to invest in Venezuela (Enter your response as a whole number) Elsewhere (30,0)
- Data on the 4000 largest mutual funds shows which funds provided a high 5-year return and a high 10-year return. Of the 4000 mutualfunds surveyed, 3000 funds had a high 5-year return, 2000 had a high 10-yearreturn, and 1500 had both a high 5-year return and a high 10-year return Given that a mutual fund had a high 5-year return, what is theprobability of a mutual fund having a high 10-year return?In the "normal version" of a game called NIM, there are two players. At the start, two piles of matches are placed on the table in front of them, each containing two matches. In turn, the players take any (positive) number of matches from one of the piles. The player taking the last match wins. Assuming optimal play, which player is sure to win in this game? O The winner cannot be determined. O Player 1 O Player 2Suppose that 30% of applicants for an industry job are proficient at object-oriented programming (OOP). Applicants are interviewed sequentially and are selected at random from the pool. Given that five applicants have already been interviewed and none of them are proficient at OOP, what is the probability that five more applicants must be interviewed to find the first individual proficient at OOP?
- Suppose that two lotteries each have 1,000 possible numbers and the same payoff. In terms of expected gain, is it better to buy two tickets from one of the lotteries or one from each?A bowl contains 7 red balls and 7 blue balls. A woman selects balls at random without looking at them. (а) How many balls must she select (minimum) to be sure of having at least three blue balls? (b) How many balls must she select (minimum) to be sure of having at least three balls of the same color?Show that 2" – (n + 1) equations are needed to establish the mutual independence of n events.
- Stick or roll is a game involving two players, A and B, and a die with four faces (numbered 1, 2, 3, 4). The faces are equally likely to occur when the die is rolled. Player A rolls the die once and sticks with that number as the score or rolls it again and scores the sum of the two numbers. • If A's score is greater than 4 then A loses. • If A's score is 4 then A wins. If A's score is less than 4, then B rolls the die once and sticks with that number as the score or rolls it again and scores the sum of the two numbers. • If B's score is greater than 4 then B loses. • If B's score is 4 or less and equal to A's or less, then B loses. • If B's score is 4 or less and greater than A's, then B wins. Player B sticks on the first roll if that number wins and rolls again if it doesn't win and it is possible to win with a second roll. Some example games might be: • A rolls a 2, chooses to roll again and rolls a 3. A's score is then 5 so A loses and B wins. * A rolls a 2 and chooses not to roll…You and your friends are playing Amogus- a social deduction game where every now andthen, someone is voted the most “sus” and knocked out of the game. There are 7 players:you are blue, and your friends are red, green, yellow, violet, orange, and gray. Of course,no game of Amogus is complete without “that one player” who just votes for someone atrandom every round and doesn’t actually play the game properly- this time, it’s the greenplayer (I won’t name names). Suppose they start a new game, so nobody has been eliminatedyet. Before the first round of voting, orange declares, “I swear, green, if you vote for me thisround, I’ll vote for you in the next round and for the rest of the game!”Before proceeding, there are a few assumptions that need to be made:• Everyone has an equal chance of being picked by green in every round (note that nobodycan vote for themself). Also, green never abstains from voting.• Orange is being serious. If green votes orange in round 1, then orange will vote…An auto insurance company classifies its customers in three categories: poor, satisfactory, and preferred. Each year, 5% of those in the poor category are moved to satisfactory and 25% of those in the satisfactory category are moved to preferred. Also, 25% in the preferred category are moved to the satisfactory category, and 25% of those in the satisfactory category are moved to the poor category. Customers are never moved from poor to preferred, or conversely, in a single year. Assuming these percentages remain valid over a long period of time, how many customers can the company expect to have in each category in the long run? Y