Random variables X_{1},X_{2},...,X_{n} are independent and identically dis

Falak Kinney 2021-10-20 Answered
Random variables X1,X2,,Xn are independent and identically distributed; 0 is a parameter of their distribution.
If X1,X2,,Xn are Normally distributed with unknown mean 0 and standard deviation 1, then XN(0,1n). Use this result to obtain a pivotal function of X and 0.
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Expert Answer

Adnaan Franks
Answered 2021-10-21 Author has 92 answers
Since X1,X2,,Xn are IID random Variables such that,
XN(0,1n)
This implies
XiN(0,1)
Now,
Pivotal function for Mean can be written as
Z=(xμ)σn=(x0)1n
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