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- Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.The best fit line for a time series, {yt : t = 1,2,...,518} is found to be f (t) = 3.4025t + 199.3715. Based on the best fit line, what is the forecast value, when t = 518?The analysis of tooth shrinkage by C. Loring Brace and colleagues at the University of Michigan’s Museum of Anthropology indicates that human tooth size is con-tinuing to decrease and that the evolutionary process has not yet come to a halt. In northern Europeans, for example, tooth size reduction now has a rate of 1% per 1000 years. a. If t represents time in years and y represents tooth size, use the condition that y = 0.99y0 when t = 1000 to find the value of k in the equation y = y0 ekt. Then use this value of k to answer the following questions. b. In about how many years will human teeth be 90% of their present size? c. What will be our descendants’ tooth size 20,000 years from now (as a percentage of our present tooth size)?
- If X is exponentially distributed with parameter λ and Y is uniformly distributed on the interval [a, b], what is the moment generating function of X + 2Y ?Assume S = $45, σ = 0.25, r = 0.05, div = 0.0, on a 45 strike call and 55 days until expiration. Given delta = 0.5502 and gamma = 0.0876, what is the delta-gamma approximation for the call price on a $0.90 stock price decline?In an effort to make the distribution of income more nearly equal, the government of a country passes a tax law that changes the Lorenz curve from y = 0.98x2.1for one year to y = 0.32x2 + 0.68x for the next year. Find the Gini coefficient of income for both years. (Round your answers to three decimal places.) after before
- The analysis of tooth shrinkage byC. Loring Brace and colleagues at the University of Michigan’s Museum of Anthropology indicates that human tooth size is continuing to decrease and that the evolutionary process has not yetcome to a halt. In northern Europeans, for example, tooth sizereduction now has a rate of 1% per 1000 years.a. If t represents time in years and y represents tooth size, usethe condition that y = 0.99y0 when t = 1000 to find thevalue of k in the equation y = y0ekt. Then use this value of kto answer the following questions.b. In about how many years will human teeth be 90% of theirpresent size?c. What will be our descendants’ tooth size 20,000 years fromnow (as a percentage of our present tooth size)?Suppose that n observations are chosen at random from a continuous pdf fY(y). What is the probability that the last observation recorded will be the smallest number in the sample? I asked this question earlier today, but didn't quite understand all of the response. P(y1<=yn)p(y2<=yn) and so on was used, but shouldn't the yn be listed first in the inequality since we want to know if yn is the smallest?Suppose that the Lorenz Curve for country A is given by yA = x 2.2 and for country B is yB = 0.3x 2 + 0.7x. Use the Gini index to determine which of the two countries has greater inequality in its income distribution.
- The following table gives the total endothermic reactions involving sodium bicarbonate Final Temperature Conditions Number of Reactions 266 K 13 271 K 60 274 K 92 Assume that reactions are independent. What is the mean of the number of reactions until the first final temperature is less than 272K? Report answer to 3 decimal places.1 Suppose that X is a stochastic process with dynamics dXt = µdt +σdWt , where W is a P-Brownian motion. The drift µ and the volatility σ are both constants. Find if there is a measure Q such that the drift of process X under Q is η(∈ R) instead of µ.The lifetime of a certain type of TV remote control is given by Y . Suppose Y has approximately exponential distribution with mean 8 years. a) Find the probability that a remote control of this type will last more than 15 years. b) Find the probability that of eight such remote controls at least one will last more than 15 years. c) What should the warranty period for these remote controls be if the manufacturer wants 85% of the remote controls to last beyond the warranty period? d) What is the moment generating function of Y .