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2) Suppose that X is a random variable having a probability density function xét, x>0 ((3²) ₁ - + xe 0, elsewhere f(x; B) = 2 ΣΕ, Χ ß 98% Confidence interval for ß if a random sample is given by 2.4, 4.6, 3.3, 3.1, 4.6, 2.2, 3.8 Show whether or not is a pivotal quantity, Explain and if yes construct a

2) Suppose that X is a random variable having a probability density function xét, x>0 ((3²) ₁ - + xe 0, elsewhere f(x; B) = 2 ΣΕ, Χ ß 98% Confidence interval for ß if a random sample is given by 2.4, 4.6, 3.3, 3.1, 4.6, 2.2, 3.8 Show whether or not is a pivotal quantity, Explain and if yes construct a

MATLAB: An Introduction with Applications
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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2) Suppose that X is a random variable having a probability density function (2) xe ở f(x; B) = Show whether or not ce 7, x>0 0, elsewhere 2 ΣΕ, Χε В 98% Confidence interval for ẞ if a random sample is given by 2.4, 4.6, 3.3, 3.1, 4.6, 2.2, 3.8 is a pivotal quantity, Explain and if yes construct a
Transcribed Image Text:2) Suppose that X is a random variable having a probability density function (2) xe ở f(x; B) = Show whether or not ce 7, x>0 0, elsewhere 2 ΣΕ, Χε В 98% Confidence interval for ẞ if a random sample is given by 2.4, 4.6, 3.3, 3.1, 4.6, 2.2, 3.8 is a pivotal quantity, Explain and if yes construct a
Expert Solution
Step 1

The probability density function (PDF) of X is specified as follows:

fXx;β=1β2xe-xβ, x>00,elsewhere=1Γ2β2x2-1e-xβ, x>00,elsewhere

Thus, from the above PDF, it can be seen that X follows a gamma distribution with parameters α=2 and β, which is unknown.

So, X~Γ2, β

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