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The random sample (X1, X2,.. X5) = (2,3,5, 10, 15) representing the duration of a paritcular type of chemical reaction (in seconds) has been observed. Suppose the observation comes from an exponential population of parameter X. 1. Find a 90% confidence interval for X; 2. To the 5 observations have been associated the following related measurements of nitrogen monoxide produced by the reaction: (4, 5, 8, 9, 13). Assume that among the observed ; and the related Y; exist a linear dependence, and that we can assume that Y; satisfy suitable normality assumptions, find the esti- mated regression coefficients and the determination coefficient.

The random sample (X1, X2,.. X5) = (2,3,5, 10, 15) representing the duration of a paritcular type of chemical reaction (in seconds) has been observed. Suppose the observation comes from an exponential population of parameter X. 1. Find a 90% confidence interval for X; 2. To the 5 observations have been associated the following related measurements of nitrogen monoxide produced by the reaction: (4, 5, 8, 9, 13). Assume that among the observed ; and the related Y; exist a linear dependence, and that we can assume that Y; satisfy suitable normality assumptions, find the esti- mated regression coefficients and the determination coefficient.

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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The random sample (X₁, X2,..., X5) = (2, 3, 5, 10, 15) representing the duration of a paritcular type of chemical reaction (in seconds) has been observed. Suppose the observation comes from an exponential population of parameter X. 1. Find a 90% confidence interval for X: 2. To the 5 observations have been associated the following related measurements of nitrogen monoxide produced by the reaction: (4, 5, 8, 9, 13). Assume that among the observed x; and the related Y; exist a linear dependence, and that we can assume that Y; satisfy suitable normality assumptions, find the esti- mated regression coefficients and the determination coefficient. 3. Suppose to have performed 100 reactions and observed X₁ = 611 and ΣX? = 45000, would you reject the hypothesis Ho: po = 7 versus H₁ : ₁ = 5 for a 5% significance level?
Transcribed Image Text:The random sample (X₁, X2,..., X5) = (2, 3, 5, 10, 15) representing the duration of a paritcular type of chemical reaction (in seconds) has been observed. Suppose the observation comes from an exponential population of parameter X. 1. Find a 90% confidence interval for X: 2. To the 5 observations have been associated the following related measurements of nitrogen monoxide produced by the reaction: (4, 5, 8, 9, 13). Assume that among the observed x; and the related Y; exist a linear dependence, and that we can assume that Y; satisfy suitable normality assumptions, find the esti- mated regression coefficients and the determination coefficient. 3. Suppose to have performed 100 reactions and observed X₁ = 611 and ΣX? = 45000, would you reject the hypothesis Ho: po = 7 versus H₁ : ₁ = 5 for a 5% significance level?
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