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

MATLAB: An Introduction with Applications
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STATISTICAL INFERENCE

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, if 0 < x < ∞
otherwise
2
0,
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).
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) = e 2, if 0 < x < ∞ otherwise 2 0, 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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