Unformatted text preview: measure their heights. Suppose the heights (in the unit of cm) are 182 166 187 196 173 188 192 164 165 185. Please ﬁnd the 95% conﬁdence interval for the average height of the population. Let us assume that the heights of the population follow a normal distribution. Problem 4: Suppose X 1 ,...,X n ∼ f ( x ) independently. For X ∼ f ( x ), 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 , and E( s 2 ) = σ 2 . 1...
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 Winter '11
 Wu
 Randomness, Cumulative distribution function, Hardware random number generator, Random Number Generator

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