Let X11 X12X1 and X21, X22X22 be two independent random samples ofsize n, and n₂ from two normal populations N(₁, 2) and N(2, 2) respectively.(d) Derive a (1-a) x 100% confidence interval for (₁-2) when both samples aresmall but of and of are known.

Let be two independent random samples of size n1 and n2 from two normal populations respectively.

Answered: Let X₁1X12X1, and X21, X22X2 be 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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Suppose data is obtained from 20 pairs of (x, y) and the sample correlation coefficient is 0.80. (a) Test the hypothesis that Ho: p = 0 against H₁ :p #0 with a = 0.01. Reject the null hypothesis. (b) Test the hypothesis that Ho: p = 0.25 against H₁: p = 0.25 with a = 0.01. Reject the null hypothesis. (c) Construct a 99% two-sided confidence interval for the correlation coefficient. Round your answer to 3 decimal places. < p < i i
Consider the simple linear regression model Y = a +Bx + E for i = 1,2,...,n. The variances of two estimators i.e. V(@) and V(B) are defined as respectively Nanersite of ARm of Select one: and V(8) +2 (+ %3! V(a) = o? %3D v(a) = o? ; and V(B) = Syx o v(a) = o (:-mnd v(A) - and V(B) = o v(a) = o? (1 + and V(B): Syx = a4 o va) = (; +)md V(f) = and V(ß) Syy %3D Syr fs fo fa 24 & 5 7 V E R Y D T-
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[8.3]
Two random variables X and Y have means X = 1 and Y=2, variances o=4 and o X and Pxy = 0.4. New random variables W and V are defined by V =−X+2Y and W = X +3Y. Find (a) the means, (b) the variances, = 1,
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Let X₁1X12X1, and X21, X22X2 be two independent random samples of size n, and n₂ from two normal populations N(₁, 0) and N(2, 2) respectively. (d) Derive a (1-a) x 100% confidence interval for (₁-2) when both samples are small but of and of are known.