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Q2 a) The measurements of the output of two units have given the following results. Assuming that both samples have been obtained from the normal population. Unit Sample Size Unit-A Unit-B 5 5 Sample mean 12.6 10.6 Sample Variance f(x) = 0.2 0.4 (i) Test whether the two population have the same variance (ii) Assuming the variance are same for both units, test the hypothesis that both units produce same measurements of output at 5% level of significance. (iii) Find the 95% confidence interval for the difference between the two means b) The probability density function of a random variable X is given by: 0 < x < 1 >= {a(1+x²) {acı = {a(1+x²) 1

Q2 a) The measurements of the output of two units have given the following results. Assuming that both samples have been obtained from the normal population. Unit Sample Size Unit-A Unit-B 5 5 Sample mean 12.6 10.6 Sample Variance f(x) = 0.2 0.4 (i) Test whether the two population have the same variance (ii) Assuming the variance are same for both units, test the hypothesis that both units produce same measurements of output at 5% level of significance. (iii) Find the 95% confidence interval for the difference between the two means b) The probability density function of a random variable X is given by: 0 < x < 1 >= {a(1+x²) {acı = {a(1+x²) 1

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Q2 a) The measurements of the output of two units have given the following results. Assuming that both samples have been obtained from the normal population. Unit Sample Size Unit-A Unit-B 5 5 Sample mean 12.6 10.6 f(x) 3 Sample Variance (i) Test whether the two population have the same variance (ii) Assuming the variance are same for both units, test the hypothesis that both units produce same measurements of output at 5% level of significance. = {acı! 0.2 0.4 (iii) Find the 95% confidence interval for the difference between the two means b) The probability density function of a random variable X is given by: ax 0<x< 1 1 < x < 2 a(1+x²) 0 other wise Find the value of a which makes f(x) a pdf.
Transcribed Image Text:Q2 a) The measurements of the output of two units have given the following results. Assuming that both samples have been obtained from the normal population. Unit Sample Size Unit-A Unit-B 5 5 Sample mean 12.6 10.6 f(x) 3 Sample Variance (i) Test whether the two population have the same variance (ii) Assuming the variance are same for both units, test the hypothesis that both units produce same measurements of output at 5% level of significance. = {acı! 0.2 0.4 (iii) Find the 95% confidence interval for the difference between the two means b) The probability density function of a random variable X is given by: ax 0<x< 1 1 < x < 2 a(1+x²) 0 other wise Find the value of a which makes f(x) a pdf.
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