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Let X₁, X2, X3, X30 be a random sample of size 30 from a population distributed with the following probability density function: f(x) = {e ², 1/0

Let X₁, X2, X3, X30 be a random sample of size 30 from a population distributed with the following probability density function: f(x) = {e ², 1/0

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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Let X₁, X₂, X3,..., X30 be a random sample of size 30 from a population distributed with the following probability density function: f(x): = otherwise Suppose that Y = 1X₁. 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). Let Z₁ = XX~N(0,1), and W₁=YYN (0,1), for i = 1,2,3,...,10, then: oy σχ i) State, with parameter(s), the probability distribution of the statistic, T = ii) Find the mean and variance of the statistic T = 21, wiz 21,2,3 iii) Calculate the probability that a statistic T = Z₁ + W₁ is at most 4. Στις 21 St, W₁² 10 iv) Find the value of ẞ such that P(T> B) = 0.01, where T = XZ₁² + 1²
Transcribed Image Text:Let X₁, X₂, X3,..., X30 be a random sample of size 30 from a population distributed with the following probability density function: f(x): = otherwise Suppose that Y = 1X₁. 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). Let Z₁ = XX~N(0,1), and W₁=YYN (0,1), for i = 1,2,3,...,10, then: oy σχ i) State, with parameter(s), the probability distribution of the statistic, T = ii) Find the mean and variance of the statistic T = 21, wiz 21,2,3 iii) Calculate the probability that a statistic T = Z₁ + W₁ is at most 4. Στις 21 St, W₁² 10 iv) Find the value of ẞ such that P(T> B) = 0.01, where T = XZ₁² + 1²
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