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Let X1, X2, ..., X48 denote a random sample of size n = 48 from the...

Let X1, X2, ..., X48 denote a random sample of size n = 48 from the uniform distribution U(?1,1) with pdf f(x) = 1/2, ?1 < x < 1. E(X) = 0, Var(X) = 1/3 Let Y = (Summation)48, i=1 Xi and X= 1/48 (Summation)48, i=1 Xi. Use the Central Limit Theorem to approximate the following probability. 1. P(1.2<Y<4) 2. P(X< 1/12)

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Answer #1

(5-a)2-12 ((1) _ (-1))2 48*0 0 variance 0.333333 For Y, mean Variance481/3 16 Using CLT, distribution is approximately normaladross the row to the rght under couTnn 0.00 and get uahle 0.0119 P(1.2 < Y < 4) 0.2234 22.34% For X, mean 0 Variance 1/3 * 1

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