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, if 0 < x <∞ otherwise 30 Suppose that Y = Σ1 X₁. 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
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, if 0 < x <∞ otherwise 30 Suppose that Y = Σ1 X₁. 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
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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Transcribed Image Text:QUESTION 1
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
e, if 0<x<∞
otherwise
30
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).
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