Suppose that X₁, X2, X3,...,Xn is a random sample of n from population X which has a chi- square distribution with one degrees of freedom. (i) Find lim Mg(t). n-00 (ii) Use the Central Limit Theorem to compute P(0.5 < X < 1.5), for n = 30. (iii) Use the Chebychev inequality to find the value of k for P(0.5 < X < 1.5), if n = 30.

MATLAB: An Introduction with Applications
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a)
Suppose that X₁, X2, X3,...,Xn is a random sample of n from population X which has a chi-
square distribution with one degrees of freedom.
(i) Find lim Mg(t).
n-00
(ii) Use the Central Limit Theorem to compute P(0.5 < X < 1.5), for n = 30.
(iii) Use the Chebychev inequality to find the value of k for P(0.5 < X < 1.5), if n = 30.
Transcribed Image Text:a) Suppose that X₁, X2, X3,...,Xn is a random sample of n from population X which has a chi- square distribution with one degrees of freedom. (i) Find lim Mg(t). n-00 (ii) Use the Central Limit Theorem to compute P(0.5 < X < 1.5), for n = 30. (iii) Use the Chebychev inequality to find the value of k for P(0.5 < X < 1.5), if n = 30.
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