4 Let random variables X and X2 be the returns of two assets where X N(, ) and N(, 2) with the common CR and 0 01 02 X2 2 (a) Show mathematically that none of X nor X2 first order stochastically dominates another (b) Show that X second order stochastically dominates X2 Authors of a computer algebra system wish to compare the speed of a new computational algorithm to the currently implemented algorithm They apply the new algorithm to 50 problems it averages 8 16 seconds with standard deviation 0 17 second The current algorithm averages 8 21 seconds on such problems Test, at 0 05 level of significance, the alternative hypothesis that the new algorithm has a lower average time than the current algorithm 0) The labor charge for repairs at an automobile service center are based on a standard time specified for each type of repair The time specified for replacement of universal joint in a drive shaft is one hour The manager reviews a sample of 30 such repairs The average of the actual repair times is 0 86 hour with standard deviation 0 32 hour Test at the 0 05 level of significance the null hypothesis that the actual mean time for this repair differs from one hour 1) A lawyer believes that a certain judge imposes prison sentences for property crimes that are longer than the state average 11 7 months He randomly selects 36 of the judge's sentences and obtains mean 13 8 and standard deviation 3 9 months Perform the test at 0 05 level of significance 2) In a recent year the fuel economy of all passenger vehicles was 19 8 mpg A trade organization sampled 50 passenger vehicles for fuel economy and obtained a sample mean of 20 1 mpg with standard deviation 2 45 mpg Test the hypothesis that the mean is greater than 20 1 at 0 05 level of significance Suppose the following is the mathematical model Max 14x s t ax 65 X0 where a is the number of hours required for each unit produced With a 5, the optimal solution is x 13 00 If we have a stochastic model with a 3, a 4, a 5, or a 6 as the possible values for the number of hours required per unit, what is the optimal value for x Round your answers for the optimal solution to two decimal places Round the answers for profit to the nearest dollar and profit $ If a 3, x If a 4, x and profit $ If a 5, x and profit $ If a 6, x and profit $ What problems does this stochastic model cause The problem with this stochastic model is with certainty and therefore the values of are not known

The Answer is in the image, click to view ...

Question: 4. Let random variables X and X2 be the returns of two assets where X ~N(, ) and N(, 2) with the common CR

4. Let random variables X and X2 be the returns of two assets where X ~N(, ) and N(, 2) with the common CR and 0 < 01

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock