2011100BHW3

# 2011100BHW3 - measure their heights Suppose the heights(in...

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STAT 100B HW III Due Friday 5pm 8971 MS Problem 1: Suppose we roll a die 1000 times, and the average of the 1000 numbers is 3.4. Is there evidence that the die is not fair? Problem 2: Suppose we generate 1000 random numbers using a random number generator in the computer. The random number generator is supposed to output random numbers that are independent and uniformly distributed over [0 , 1]. If the average of these 1000 number is .53. Is there evidence that there is something wrong with this random number generator? Problem 3: Suppose we randomly sample 10 people from the population of adult males, and we
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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 n-1 n X i =1 ( X i-¯ X ) 2 . Prove E[ ¯ X ] = μ , and E( s 2 ) = σ 2 . 1...
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