Assuming that on an average 1% of the output in a factory making certain part of an article are defective and that 200 units are in a package, find the probabilities that (a) At most 2 defectives (b) At least 2 defectives may be found in the package. (e2 = 0.1353) %3D
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- In game of roulette, a player can bet on the 1/38 probabilty of metal batt landa on 1the player gets to keep the paid to play the game and the player is awarded an additional 140 Otherwise, the player is awarded nothing and the casino takes the player's $4. Find the expected value E(x) to the player for one play of the game to player in a game of chance, then E(x) is negative. This value gives the average amount the player can expect to lose.3. Suppose Chelsea has the following utility function over sure wealth: v (y) = In y (a) Consider the lottery that yields the outcome $2 with probability and the outcome $8 with probability . What is Chelsea's certainty equivalent for this lottery? 2 3* (b) For the lottery in (b), how much would Chelsea pay to have her risk taken away? (c) What is Chelsea's probability premium at $25 for a lottery that could swing her wealth $20 up or down? What about $15 up or down?When it is sunny, Joe's ice cream truck generates a profit of $547 per day, when it is not sunny, the profit is $250 per day, and when the truck is not out there selling ice cream, Joe loses $120 per day. Suppose 8% of a year Joe's truck is on vacation, and 86% of a year the truck is selling ice cream on sunny days, what is the expected daily profit the truck generates over a year? Enter answer as a decimal rounded to TWO digits after the decimal point.
- . The probability that a newborn life (age 0) survives x years is given by: 110 - x xPo 0Assume that W (t) is a standard Brownian motion and that S(t) is a random variable defined as S(t) = 8 · 2W(t). Determine9If X is exponentially distributed, prove that the probability that X exceed its expected value is less than 0.5In the transmission of digital information, the probability that a bit has high, moderate, and low distortion is 0.01, 0.04, and 0.95, respectively. Suppose that three bits are transmitted and that the amount of distortion of each bit is assumed to be independent. Let X and Y denote the number of bits with high and moderate distortion out of the three, respectively. Determine: (c) E(X)= i Round your answer to two decimal places (e.g. 98.76).A family purchases a 2000 square foot home and plans to make extensions totalling 500 square feet. The house currently has a pool, and a real estate agent has reported that the house is in excellent condition. However, the house does not have a view, and this will not change as a result of the extensions. According to the results in column (1), what is the expected DOLLAR increase in the price of the home due to the planned extensions?4. An insurance company sells an automobile policy with a deductible of one unit. Let X be the amount of the loss having pmf 0.9 f(x) = x = 0 x = 1,2,3,4,5,6 where c is a constant. a) Find c. b) Find the expected value of the amount the insurance company must pay.If the life expectacy in county A is 65 years with CI of (55, 75) and in county B is 87 years with CI of (40, 98), are the two life expectancies likely to be statistically different?P(-0.34SEE MORE QUESTIONSRecommended textbooks for youMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons Inc
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