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

Random variables ${X}_{1},{X}_{2},\dots ,{X}_{n}$ are independent and identically distributed; 0 is a parameter of their distribution.
If ${X}_{1},{X}_{2},\dots ,{X}_{n}$ are Normally distributed with unknown mean 0 and standard deviation 1, then $\stackrel{―}{X}\sim N\left(\frac{0,1}{n}\right)$. Use this result to obtain a pivotal function of X and 0.
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Since ${X}_{1},{X}_{2},\dots ,{X}_{n}$ are IID random Variables such that,
$\stackrel{―}{X}\sim N\left(0,\frac{1}{n}\right)$
This implies
${X}_{i}\sim N\left(0,1\right)$
Now,
Pivotal function for Mean can be written as
$Z=\frac{\left(\stackrel{―}{x}-\mu \right)}{\frac{\sigma }{\sqrt{n}}}=\frac{\left(\stackrel{―}{x}-0\right)}{\frac{1}{\sqrt{n}}}$