please help me with probability HW, i will rate the best answer, thank you very much. if you're not sure with your answer please do me a favor and let someone else do it cus i can only post the question once. i appreciate the help !
Let us denote
To find which confidence interval is shorter, suppose is a confidence interval. Then, the length of the interval is .
The minimization problem is
minimize
Subject to
Using Lagrange multiplier, the conditions are,
Now, using Fundamental Theorem of calculus,
Substituting in equations (1) and (2),
Adding equations (3) and (4), we get
does not make any sense. So
Thus the interval is shorter than
Here
Proof is complete.
please help me with probability HW, i will rate the best answer, thank you very much....
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