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a) Let X₁, X₂, X3, X30 be a random sample of size 30 from a population distributed with the following probability density function: f(x) = 2 if 0

a) Let X₁, X₂, X3, X30 be a random sample of size 30 from a population distributed with the following probability density function: f(x) = 2 if 0

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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a) Let X₁, X₂, X3..., X30 be a random sample of size 30 from a population distributed with the following probability density function: f(x) = if 0<x<∞ otherwise Suppose that YΣX₁. Use = i) the moment generating function technique to find the probability distribution function of Y. Write down the density function of Y. ii) the Central Limit Theorem to compute P(40 <Y <80). iii) the Chebychev inequality to find the lower bound of P(40<Y <80). b) Let Z₁-N (0,1), and W₁=~N(0,1), for i = 1,2,3,...,10, then: = dx i) State, with parameter(s), the probability distribution of the statistic, T = 2 ii) Find the mean and variance of the statistic T = 16 iii) Calculate the probability that a statistic T = Z₁ + W₁ is at most 4. iv) Find the value of such that P(T> B) = 0.01, where T = 1, Z²+1, W².
Transcribed Image Text:a) Let X₁, X₂, X3..., X30 be a random sample of size 30 from a population distributed with the following probability density function: f(x) = if 0<x<∞ otherwise Suppose that YΣX₁. Use = i) the moment generating function technique to find the probability distribution function of Y. Write down the density function of Y. ii) the Central Limit Theorem to compute P(40 <Y <80). iii) the Chebychev inequality to find the lower bound of P(40<Y <80). b) Let Z₁-N (0,1), and W₁=~N(0,1), for i = 1,2,3,...,10, then: = dx i) State, with parameter(s), the probability distribution of the statistic, T = 2 ii) Find the mean and variance of the statistic T = 16 iii) Calculate the probability that a statistic T = Z₁ + W₁ is at most 4. iv) Find the value of such that P(T> B) = 0.01, where T = 1, Z²+1, W².
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