# Random variables X_{1},X_{2},...,X_{n} are independent and identically distributed. 0 is a parameter of their distribution. If q(X,0)\sim N(0,1) is a pivotal function for 0, explain how you would use this result to obtain a symmetrical 95% confidence interval for 0.

Random variables ${X}_{1},{X}_{2},...,{X}_{n}$ are independent and identically distributed. 0 is a parameter of their distribution.
If $q\left(X,0\right)\sim N\left(0,1\right)$ is a pivotal function for 0, explain how you would use this result to obtain a symmetrical 95% confidence interval for 0.
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If $q\left(X,0\right)\sim N\left(0,1\right)$ is the Pivotal function for θ,
This implies the 95% confidence interval can be given by
$P\left({Z}_{0.025}\right)$
Now simplify this expression until an expression of this kind is obtained
$P\left({Z}_{0.025}×A<0\right)$
Where A and B are constants.
For example, for the pivotal function formed in (b), Confidence Interval can be given by
$P\left(\stackrel{―}{x}+{Z}_{0.025}×\frac{\sigma }{n}<0<\stackrel{―}{x}+{Z}_{0.975}×\frac{\sigma }{n}\right)=0.95$
The confidence interval is
$\left(\stackrel{―}{x}-1.96×\frac{\sigma }{n},\stackrel{―}{x}+1.96×\frac{\sigma }{n}\right)$