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- A function has a graph which passes through the point (2,3) and its graph also has the property that the normal line to each point (x,y) on the graph passes through the point (2,0). Find the function?For least-squares to work well, we need: ) the relationship between x and y to be non-linear. residuals to be Uniformly distributed. ) the residuals to have a mean of zero. the residuals to be correlated with the explanatory variable.Assume that we collect data (time how late the bus was at the end of the day) in related to following problem. A bus is scheduled to stop at a certain stop every half hour. At the end of the day due to delays that often occur earlier in the day, the bus is likely to be late. The director of the bus line claims that the length of time a bus is late at the end of the day is uniformly distributed and the maximum time that a bus is late is 20 minutes. Assume the lateness of the bus on different days are independent. (a) In a randomly selected day, what is the probability this bus is late more than 5 minutes at the end of the day? If we consider consecutive days, what is the probability that the 6th day will be first (b) day this bus is late more than 5 minutes at the end of the day? What is the probability that at least 10 consecutive days there, before a day with this bus is late more than 5 minutes at the end of the day? (d) . probability that less than 60 of them will be more than 5…
- The amount of time it takes Susan to wait for the bus is continuous and uniformly distributed between 4 minutes and 18minutes. What is the probability that it takes Susan less than 5 minutes given that it takes less than 11 minutes for her to wait for the busTwo points are selected randomly on a line segment of length 20, one on each side of the midpoint of the line. That is, the two points X and Y are independent random variables such that X is uniformly distributed over (0, 10) and Y is uniformly distributed over (10, 20). Find the probability that the distance between the two points is greater than 8. Hint: Think of the pair (X, Y) as a point on the x-y plane (as in the Mr. Johnson and the newspaper problem) and identify the region where they're more than 8 apart..let Y=5X+10 and X be normally distributed with a mean 10 and varience 25. find P(Y<54).
- The Volatility X for the S&P stock index on a given day is a normal random variable with mean = 10 and standard deviation = 2 The volatilities recorded over a 100-day period on the S&P500 are Y1, Y2, ... Y100. Assume that these Yi's are independent and identically distributed, uniform on the interval [5,15]. Let V = (Y1 + Y2 + ... + Y100)/100. What approximately is P[9.5 < V < 10.5]?2.Suppose that the return R (in dollars per share) of a stock has the uniform distribution on the interval [-3,7]. Suppose also, that each share of the stock costs $1.50. Let Y be the net return (total return minus cost) on an investment of 10 shares of the stocks. Compute E(Y).In a continuous-time surplus model, the claim severity is distributed as BN(2, 0.4). Determine the Lundberg upper bound for the probability of ultimate ruin if the initial surplus is 2 and the prIn a continuous-time surplus model, the claim severity is distributed as BN(2, 0.4). Determine the Lundberg upper bound for the probability of ultimate ruin if the initial surplus is 2 and the premium loading factor is 0.25.emium loading factor is 0.25.
- Let X have a uniform distribution on the interval (2, 9). Find the probability that the sum of 2 independent observations of X is greater than 16.Let Y1, Y2,., Ya be a collection of independent random variables with distribution function y 8 Show that Y converges in probability to a constant, and provide that constant. 1The time (in minutes) between arrivals of customers to a post office is to be modelled by the Exponential distribution with mean 0.62. a) find the P(10<x<15) (10 and 15 are seconds) b) find the P(x>15| x>10) (10 and 15 are seconds) c) find the P(x<15) (15 is seconds)