a) Let X₁, X₂, X3, X30 be a random sample of size 30 from a population distributed with the following probability density function: ¹e, 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)
-**
if 0 < x <∞
otherwise
Suppose that Y = Σ₁X₁. 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).
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 Y = Σ₁X₁. 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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