Question: A sequence ofn= 10 random numbers is generated by a student from an unknown distribution with support [0,5]. Suppose the numbers are {0.2,1.3,3.5,2.4,4.5,3.6,2.5,1.4,0.9,2.3}. Suggestion:You are

A sequence ofn= 10 random numbers is generated by a student from an unknown distribution with support [0,5]. Suppose the numbers are

{0.2,1.3,3.5,2.4,4.5,3.6,2.5,1.4,0.9,2.3}.

Suggestion:You are recommended to write down the formula first so you don't lose much points if you have miscalculated.

(i) Compute the sample meanXnand the unbiased sample variancen2. [5]

n(ii) Construct an unbiased estimator for the second moment,E[X2]. Denote it byX2.

Compute it.

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