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Suppose i) the moment generating function technique to find the probability distribution Write down the density function of Y. ii) the Central Limit Theorem to compute P(40

Suppose i) the moment generating function technique to find the probability distribution Write down the density function of Y. ii) the Central Limit Theorem to compute P(40

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: S b) Suppose that Y = ΣX₁. 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 Z -N(0,1), for i=1,2,3,...,10, then: a f(x) = Xx N (0,1), and W OX e, if 0 < x <∞ otherwise Σε St, w₁² i) State, with parameter(s), the probability distribution of the statistic, T = 21=1 ii) Find the mean and variance of the statistic T 10 V10 41=1 212 iii) Calculate the probability that a statistic T = Z, +W, is at most 4. 6°C
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: S b) Suppose that Y = ΣX₁. 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 Z -N(0,1), for i=1,2,3,...,10, then: a f(x) = Xx N (0,1), and W OX e, if 0 < x <∞ otherwise Σε St, w₁² i) State, with parameter(s), the probability distribution of the statistic, T = 21=1 ii) Find the mean and variance of the statistic T 10 V10 41=1 212 iii) Calculate the probability that a statistic T = Z, +W, is at most 4. 6°C
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