Unformatted text preview: θ/ ( θ + 1). 4. Consider a random sample of size 72 from the distribution with pdf f ( x ) = 1 x 2 I (1 , ∞ ) ( x ). Compute the approximate probability that more than 50 of the observations are less than 3. 5. Suppose that a random sample of size 10, taken from the N ( μ, 2) distribution, results in a sample mean of 7 . 4. Give an 80% conFdence interval for the true mean μ . 6. Required for 5520 Students Only: Let X 1 , X 2 , . . . , X n be a random sample from any distribution with variance σ 2 . Assume that the Frst four moments, μ k = E [ X k ], k = 1 , 2 , 3 , 4, of this distribution exist. Show that S 2 P → σ 2 . where S 2 is the sample variance S 2 = ∑ n i =1 ( X iX ) 2 n1 ....
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 Fall '11
 Manuel
 Normal Distribution, Probability theory, X1

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