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- 1) Assuming you have a data matrix X that has n rows and p variables and you know both µ and Σ. How is (X- µ)‘Σ-1(X- µ) distributed? 2) Assuming that you don’t know the values of µ and Σ. How is the statistical distance distributed as n-p gets large?If two stocks have variance σ2=16 each, could their covariance be equal to σ12 = 202. A leading researcher in the study of interstate highway accidents proposes that a major cause of many collisions on the interstates is not the speed of the vehicles but rather the difference in speeds of the vehicles. When some vehicles are traveling slowly while other vehicles are traveling at speeds greatly in excess of the speed limit, the faster-moving vehicles may have to change lanes quickly, which can increase the chance of an accident. Thus, when there is a large variation in the speeds of the vehicles in a given location on the interstate, there may be a larger number of accidents than when the traffic is moving at a more uniform speed. The researcher believes that when the standard deviation in speed of vehicles exceeds 10 mph, the rate of accidents is greatly increased. During a 1-hour period of time, a random sample of 50 vehicles is selected from a section of an interstate known to have a high rate of accidents, and their speeds are recorded using a radar gun. The data…
- Mike, a lumber wholesaler, is considering the purchase of a (railroad) car- load of varied dimensional lumber. He calculates that the probabilities of reselling the load for $10,000, $9000, and for $8000 are 0.22, 0.33, and 0.45 respectively. In order to ensure an expected profit of $3000, how much can Mike pay for the loadYou and two other people are to place bids for an object, with the high bid winning. If you win, you plan to sell the object immediately for 10,000.(a) How much should you bid to maximize your expected profit if you believe that the bids of the others can be regarded as being independent and uniformly distributed between 7,000 and 10,000?Show that (X+1)/(n+2) is a biased estimator of the binomial parameter θ. Is this estimator asymptotically unbiased?
- Suppose a sample of 950 men found that 642 of them favored the death penalty for capital murder convictions while a sample of 810 women found that 405 of them favored the death penalty for capital murder convictions. Test the claim using a signifiance level of 0.05 that the proportion of men favoring the death penalty is greater tha nthe proportion of women favoring the death penalty. Let p1 = proportion of men favoring the death penalty Let p2 = proportion of women favoring the death penalty Answer the following questions below based upon the above data and the definitions of p1 and p2 Which group of statements correctly describe the Claim, the Null Hypothesis, and the Alternative Hypothesis:Suppose a sample of 950 men found that 642 of them favored the death penalty for capital murder convictions while a sample of 810 women found that 405 of them favored the death penalty for capital murder convictions. Test the claim using a signifiance level of 0.05 that the proportion of men favoring the death penalty is greater tha nthe proportion of women favoring the death penalty. Let p1 = proportion of men favoring the death penalty Let p2 = proportion of women favoring the death penalty Answer the following questions below based upon the above data and the definitions of p1 and p2 a) What is the type of Test? b) What is/are the critical values(s) c) What is the value of the test statistic? d) What is the decision? e) What is the conclusion?One car manufacturer produces different models of cars in 4 different factories. Total production; 30% 1. factory 20% 2. factory 22% 3. factory 28% is realized in 4 factories. Only the rates at which a particular model is produced in these factories 1. factory %5, 2.factory %7, 3. factory %10, 4. factory 2 % How much is the production rate of a particular model in the entire production of the company? How likely is it that any car from the specified model we see on the street was produced at 1. factory or at 2. factory?
- 1- The number of items produced in a factory during a week is known to be a randomvariable with mean 50● Using Markov's inequality, what can you say about the probability that this week'sproduction exceeds 75?● If the variance of one week's production is equal to 25, then using Chebyshev'sinequality, what can be said about the probability that this week's production isbetween 40 and 60?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.Southwestern Electronics has developed a new calculator that performs a series offunctions not yet performed by any other calculator. The marketing department isplanning to demonstrate this calculator to a group of potential customers, but it isworried about some initial problems, which have resulted in 4 percent of the newcalculators developing mathematical inconsistencies. The marketing VP is planningon randomly selecting a group of calculators for this demonstration and is worriedabout the chances of selecting a calculator that could start malfunctioning. Hebelieves that whether or not a calculator malfunctions is a Bernoulli process, and heis convinced that the probability of a malfunction is really about 0.04. Assuming thatthe VP selects exactly 50 calculators to use in the demonstration, and using thePoisson distribution as an approximation of the binomial, what is the chance ofgetting at least three calculators that malfunction?