Let X 1 , , X n X 1 , , X n be iid
Question:
Let X1,…,Xn be iid random variables having continuous uniform distributions of the form f(z)=I(0,1)(z).
(a) Define an asymptotic distribution for ¯Xn=n−1∑ni=1Xi.
(b) Using your result from (a), argue that (∑12i=1Xi)−6≈Z∼N(0,1).
(This approximation is very accurate, and is sometimes used for simulating N(0,1) outcomes using a uniform random number generator.)
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SOLUTION a By the Central Limit Theorem as n increases the ...View the full answer
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Related Book For
Mathematical Statistics For Economics And Business
ISBN: 9781461450221
2nd Edition
Authors: Ron C.Mittelhammer
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