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- Problem 4-05 (Algorithmic) In American football, touchdowns are worth 6 points. After scoring a touchdown, the scoring team may subsequently attempt to score 1 or 2 additional points. Going for 1 point is virtually an assured success, while going for 2 points is successful only with probability p. Consider the following game situation. The Temple Wildcats are losing by 14 points to the Killeen Tigers near the end of regulation time. The only way for Temple to win (or tie) this game is to score two touchdowns while not allowing Killeen to score again. The Temple coach must decide whether to attempt a 1-point or 2-point conversion after each touchdown. If the score is tied at the end of regulation time, the game goes into overtime. The Temple coach believes that there is a 43% chance that Temple will win if the game goes into overtime. The probability of successfully converting a 1-point conversion is 1.0. The probability of successfully converting a 2-point conversion is p. Assume…Please help answer the following: Suppose that we have designed a randomized algorithm for a problem having “Yes” or “No” answer. The algorithm is such that if the answer is “Yes,” it is always correct. If the answer is “No,” it is correct withprobability at least 0.02. How many times do we need to run this algorithm in order to be sure that the probability of getting an erroneous answer is at most 0.02? **ASAP** (will leave a thumbs up)PROBLEM (8) A risk averse decision maker with u(x) = square root(x) faces a lottery L that delivers $2500 or $100 with equal (1/2) probabilities. (a) Would he choose the lottery or a sure reward of $901 ?(b) Now suppose that he can buy “2 copies” of the lottery; this means there are 2 lotteries like above where the random prizes for each lottery is drawn independently with the probabilities above, and the sum reward from two lotteries is to be paid to the decision maker. Would the agent choose this “bundled lottery” or a sure reward of 2 x $901 = $1802 ? As you see, when the risk is independently replicated, the agent is less risk averse against aggregate risk that is composed of many “idiosyncratic risks”. PLEASE ANSWER ALL THE PARTS!
- PROBLEM (8) A risk averse decision maker with u(x) = square root(x) faces a lottery L that delivers $2500 or $100 with equal (1/2) probabilities. (a) Would he choose the lottery or a sure reward of $901 ?(b) Now suppose that he can buy “2 copies” of the lottery; this means there are 2 lotteries like above where the random prizes for each lottery is drawn independently with the probabilities above, and the sum reward from two lotteries is to be paid to the decision maker. Would the agent choose this “bundled lottery” or a sure reward of 2 x $901 = $1802 ? As you see, when the risk is independently replicated, the agent is less risk averse against aggregate risk that is composed of many “idiosyncratic risks”. PLEASE ANSWER ALL THE PART!Problem 1 One of the advantages that concrete structures have over steel structures is fire resistance (which is to say, steel becomes weak when heated). The time, T, that it takes a steel girder to reach certain temperature (where its strength becomes too low to support its load) in a fire is, however, random. Suppose that for design code development, the following data have been gathered on the time T in hours: 0.736, 0.863, 0.865, 0.913, 0.915, 0.937, 0.983, 1.007, 1.011, 1.064, 1.109, 1.132, 1.140, 1.153, 1.253, 1.394 (a) Compute the values of the sample mean and the sample median by hand. (b) By how much could the smallest sample observation be increased without affecting the value of the sample median? (c) By how much could the smallest sample observation be increased without affecting the value of the sample mean? (d) Compute the values of the first quartile, third quartile, interquartile range, lower fenceProblem 15-9 (Algorithmic) Marty's Barber Shop has one barber. Customers have an arrival rate of 2.2 customers per hour, and haircuts are given with a service rate of 4 per hour. Use the Poisson arrivals and exponential service times model to answer the following questions: What is the probability that no units are in the system? If required, round your answer to four decimal places.P0 = What is the probability that one customer is receiving a haircut and no one is waiting? If required, round your answer to four decimal places.P1 = What is the probability that one customer is receiving a haircut and one customer is waiting? If required, round your answer to four decimal places.P2 = What is the probability that one customer is receiving a haircut and two customers are waiting? If required, round your answer to four decimal places.P3 = What is the probability that more than two customers are waiting? If required, round your answer to four decimal places.P(More than 2 waiting) = f…
- Question 3 A political candidate wants to enter a primary in a district with 100,000 eligible voters, but only if he has a good chance of winning. He hires a survey organization, which takes a simple random sample of 1600 voters. In the sample, 880 favor the candidate, so the percentage is 55%. This is good news but we need to understand the chance error. To find out the standard error, we need the SD of the box. But to compute this, we need the actual2. Each of 12 refrigerators of a certain type has been returned to a distributor because of the presence of a high-pitched oscillating noise when the refrigerator is running. Suppose that four of these 12 have defective compressors and the other eight have less serious problems. If they are examined in random order, let ? be the number among the first six examined that have a defective compressor. Compute (a) ?(? = 1), (b) ?(? ≥ 4), and (c) ?(1 ≤ ? ≤ 3).Question 3 Two software consulting firms V and W consider bidding on a large programmingproject, which may or may not be awarded depending on the amounts of the bids. Firm Vsubmits a bid and the probability is 3/4 that it will get the project provided that firm W does notbid. The probability is 3/4 that W will bid, and if it does, the probability that V will get theproject is 1/3.(a) What is the probability that V will get the project?(b) If V gets the project, what is the probability that W did not bid?
- Use for questions 1-5: An imaging scientist wishes to determine whether the intensity of light has an effect on the ability of their algorithm to recognize a particular target. Considering only daytime recognition, the scientist classifies the light source as being high or low intensity and performs a series of randomly chosen recognition tests. The outcome of each test is either positive (recognized) or negative (not recognized). The following data is observed: High Intensity Low Intensity Positive Recognition 36 9 Negative Recognition 24 31 What is the EXPECTED COUNT for the cell that has 36 in it (Positive and High)? The answer is an integer. What is the Chi-Square Contribution for the cell with 36 (positive and high)? The answer is an integer. The test statistics follows a Chi-Square Distribution with how many degrees of freedom? The value of the test statistic is . Calculate the p-value. (ROUND TO 4 DECIMAL PLACES!!!)Rework problem 15 from section 1.4 of your text, involving the selection of rats from a cage. Assume that there are 7 rats in the cage: 5 trained and 2 untrained. A rat is removed from the cage and it is noted whether or not it is trained. It is then placed in a different cage. 5 more rats are removed and treated the same way. How many outcomes are possible for this experiment?Problem 2. Last year, in a sample of 1200 randomly selected consumers who had opportunities to send in a rebate claim form after purchasing a product A, there are 300 of these people said they never did. This year, if a consumer sends in a rebate claim form, he will get 5 reward points. Observe 1000 randomly selected consumers who had opportunities to send in a rebate claim form after purchasing a product A this year, 200 of these people said they never did. a/ Does this data strongly suggest that the true proportion of such consumers who never apply for a rebate claim after purchasing the product A last year is greater than this year? Test the hypotheses at significance level 0.05 b/ Calculate an lower confidence bound at the 97% confidence level for the true proportion of such consumers who never apply for a rebate claim after purchasing the product A this year