Suppose that P, and P2 are two populations having bivariate normaldistributions with mean vectorsand (), respectively, and the same(0.75variance-covariance matrix (O ). Let Z, = () and Z2 = 5) be(0.25)0.25%3D\0.51two new observations. If the prior probabilities for P, and P2 are assumed to beequal and the misclassification costs are also assumed to be equal then,according to linear discriminant rule,Z, is assigned to P, and Z2 is assigned to P2Z, is assigned to P2 and Z, is assigned to Pboth Z, and Z2 are assigned to P1both Z, and Z2 are assigned to P2(A)(B)(C)(D)

Let q1 and q2 be the prior probabilities for P1 and P2. It is given that q1 and q2 are equal i.e q1…

Answered: Suppose that P, and P2 are two…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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What is the covariance matrix V for M = 3 independent experiments with means m1, m2, m3 and variances a-r, (T�, O"§ ?
Suppose the random variables X and Y are inde lent and identically distributed. Let Z =aX +Y. If the correlation coefficient between X and Z is1/3 , then what is the value of the constant a ?
The management of a supermarket wants to adopt a new promotional policy of giving free gift to every customer who spends more than a certain amount per visit at this supermarket. The expectation of the management is that after this promotional policy is advertised, the expenditure for all customers at this supermarket will be normally distributed with mean 400 L.E and a variance of 900 L.E2. 1) If the management wants to give free gifts to at most 12% of the customers, what should the amount of expenditure be above which a customer would receive a free gift? 2) In a sample of 100 customers, what is the number of customers whose expenditure is between 420 L.E and 485 L.E? 3) What is a probability of selecting a customer whose expenditure is differ than the population mean expenditure by at most 50 L.E? 4) What is the percentage of customers whose expenditure is at least 450 L.E.?
The management of a supermarket wants to adopt a new promotional policy of giving free gift to every customer who spends more than a certain amount per visit at this supermarket. The expectation of the management is that after this promotional policy is advertised, the expenditure for all customers at this supermarket will be normally distributed with mean 400 L.E and a variance of 900 L.E2.1) If the management wants to give free gifts to at most 12% of the customers, what should the amount of expenditure be above which a customer would receive a free gift?
Find the marginal probabilities of each random variable X and Y in thefollowing table:- Compute the covariance and the correlation of these two random variables.
If X1, X2, and X3 constitute a random sample of sizen = 3 from a normal population with the mean μ and thevariance σ2, find the efficiency of X1 + 2X2 + X34relative toX1 + X2 + X33as estimates of μ.
IfX1 andX2 are the means of independent random samples of sizes n1 and n2 from a normal population with the mean μ and the variance σ ^2 , show that the variance of the unbiased estimator ω·Xbar1+(1−ω)·Xbar2is a minimum whenω=n1/(n1+n2)
Suppose that a portfolio consists of two assets A and B whose returns are givenby RA = RM + uA and RB = 2RM + uB, where RM is the market return, which isuncertain, and where uA and uB are uncorrelated shocks with expected value of zeroand variance of 0.01. Suppose RM has expected value of 0.05 and a variance of 0.01. Calculate theexpected return and variance of both assets A and B.
The records of a casualty insurance company show that, in the past, its clients have had a mean of 1.9 auto accidents per day with a variance of 0.0036. The actuaries of the company claim that the variance of thenumber of accidents per day is no longer equal to 0.0036. Suppose that we want to carry out a hypothesis test to see if there is support for the actuaries' claim. State the null hypothesis H0 and the alternative hypothesis H1 that we would use for this test.
A finance analyzer have come to the conclusion that he wants to purchase stocks from Company A, with an expected yield of E(X) = 4% and variance to the yield being V(X) = 0.49. Another stock from another Company B have an expected yield of E(Y) = 6% and variance V(Y) = 0.64. The correlation of the yield between the two stocks is p(X,Y) = 0.3. The finance analyzer wants to invest a portion p(0 < p < 1) into Company A stocks, and the rest (1 - p) into company B stocks. The combined investment have a yield of W = pX + ( 1 - p)Y. For p = 0.4, such that W = 0.4X + 0.6Y. What is the expected value and variance for W.
2, For the three clusters identified in the accompanying Distance Matrix After Second Clustering table, find the average and standard deviations of each numerical variable for the schools in each cluster and compare them with the average and standard deviation for the entire data set. Does the clustering show distinct differences among these clusters? Compute the overall mean and overall standard deviation for each numerical variable. Median SAT Acceptance Rate Expenditures /Student Top 10% HS Graduation % Overall Mean enter your response here enter your response here% $enter your response here enter your response here enter your response here Overall Stdev enter your response here enter your response here% $enter your response here enter your response here enter your response here (Round to two decimal places as needed. Type N if the solution is undefined.) Colleges and Universities School…
A U.S. Food Survey showed that Americans routinely eat beef in their diet. Suppose that in a study of 49 consumers in Illinois and 64 consumers in Texas the following results were obtained from two samples regarding average yearly beef consumption: Illinois Texas = 49 = 64 = 54.1lb = 60.4lb S1 = 7.0 S2 = 8.0 Formulate a hypothesis so that, if the null hypothesis is rejected, we can conclude that the average amount of beef eaten annually by consumers in Illinois is significantly less than that eaten by consumers in Texas.

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