a) Let X₁, X₂.X3X30 be a random sample of size 30 from a population distributed with the following probability density function: e-ž, if 0

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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<x<∞
otherwise
Suppose that Y = ΣX₁. Use
30
#1
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).
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)=2 if 0<x<∞ otherwise Suppose that Y = ΣX₁. Use 30 #1 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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