a) Suppose that X₁, X₂, X3,...,X₁ is a random sample of n from population X which has a chi- square distribution with one degrees of freedom. (i) Find lim MX(t). 1400 (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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Suppose that X₁, X₁, X3,...,X₂ is a random sample of n from population X which has a chi-
square distribution with one degrees of freedom.
(i) Find lim MX(t).
110
(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:Suppose that X₁, X₁, X3,...,X₂ is a random sample of n from population X which has a chi- square distribution with one degrees of freedom. (i) Find lim MX(t). 110 (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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