Conditional upon an unknown scientifific constant , let X f be iid random variables representing the future
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Question:
Conditional upon an unknown scientifific constant, letX fbe iid random variables
representing the future outcomes of a series of experiments, with E(Xi) =units and
Var(Xi) = 400 squared units. The estimator forwill beX=i=1nXi/n . Assuming that
the CLT applied with suffiffifficiently fast convergence,
(a) (8 marks) What is the probability that the realisation ofX will be within 1 unit of
when
i.n= 1?
ii.n= 4?
iii.n= 16?
iv.n= 100?
(b) (2 marks) If the experimenter asks you what is the least number of experiments that
should be performed in order to have a probability of at least 0.95 thatX will be
within 2 units of, what do you reply?
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