Unformatted text preview: 165 185. Let us assume that the heights of the population follow a normal distribution N ( μ,σ 2 ). (1) Calculate the sample variance s 2 . (2) Test the hypothesis H : μ = 180 versus H 1 : μ > 180. (3) Find the 95% conﬁdence interval for the average height of the population. Problem 4: Suppose X 1 ,...,X n ∼ f ( x ) independently. Let μ = E[ X ], and σ 2 = Var[ X ]. Let ¯ X = 1 n n X i =1 X i , and s 2 = 1 n1 n X i =1 ( X i¯ X ) 2 . Prove E[ ¯ X ] = μ , Var[ ¯ X ] = σ 2 /n , and E( s 2 ) = σ 2 . 1...
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 Spring '11
 Wu
 Variance, Randomness, Hardware random number generator, µ, Random Number Generator

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