1. Let x1, x2 and x3 be the excess of heights of father, mother and son respectively in 100samples above their respective mean values in cm. A distribution of these variables gave the followingcorrelation coefficients r, between x, and x; and standard deviations o; = v V(x) for i, j = 1, 2, 3;rijr12 = 0:3,23 = 0-4,131 = 0:50, = 3,0, = 2,Oz = 4Obtain a regression equation of x, on x, and x3, and estimate the excess of height of father when excessof heights of mother and son are 0-7 cm and 2·1 cm respectively.

Answered: Image /qna-images/answer/9b5008f2-a047-462d-911b-a45cc58e392b.jpg

Answered: 1. Let x, x2 and x3 be the excess of…

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 Discrete Variable Standard Deviation for the following numbers:x = 0 and P(X = x) = 0.51x = 1 and P(X = x) = 0.11x = 2 and P(X = x) = 0.09x = 3 and P(X = x) = 0.16x = 4 and P(X = x) = 0.13
7 Let X1,...Xn be iid Normal( θ+ c, σ^2), where c and σ ^2 are known constants (i.e., E(Xi) = θ + c). Find a sufficient statistic forθ then obtain the minimum-variance unbiased estimator for θ.
(b)A random variable is defined as 172⁄(3X+1); X = 0 ,1,2,3,4,5,6. Construct the PDF of X, and comment analytically onthe variability of the given computed var(X).
If you let X1, X2, X3, X4 equal the cholesterol level of a woman under the age of 50, a man under 50, a woman 50 or older, and a man 50 or older, respectively. Assuming the distribution of Xi is N(μi, σ2), i = 1, 2, 3, 4 and you test the null hypothesis H0: μ1 = μ2 = μ3 = μ4, using seven observations of each Xi, what would be the critical region for an alpha = 0.05 significance level?
2. Suppose that at a gas station the daily demand for regular gasoline is normally distributed with a mean of 1000 gallons and a standard deviation of 100 gallons. The station manager has just opened the station for business and there is exactly 2300 gallons of regular gasoline in storage. The next delivery is scheduled later tomorrow at the close of business. (a) Let X1 and X2 denote the demand of today and tomorrow, respectively. Let X = X1 + X2. Find the distribution of X. (b) Find the probability that the manager will have enough regular gasoline to satisfy today’s and tomorrow’s demand.
A shipping company handles containers in three different sizes: (1) 27 ft3(3 × 3 × 3), (2)125 ft3, and (3) 512 ft3. Let Xi(i = 1, 2, 3) denote the number of type i containers shipped during a given week. With µi = E(Xi) and σi2 = V(Xi), suppose that the mean values and standard deviations are as follows: μ1 = 200 μ2 = 250 μ3 = 100σ1 = 10 σ2 = 12 σ3 = 8a. Assuming that X1, X2, X3 are independent, calculate the expected value and variance of the total volume shipped. [Hint: Volume = 27X1 + 125X2 + 512X3.]b. Would your calculations necessarily be correct if the Xi ’s were not independent? Explain.

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