Elianna Lawrence

Elianna Lawrence

Answered

2022-07-19

Assume I have an independent X 1 , X 2 , , X n with X i N ( i , i 2 ) and I want to find a statistic that has a t distribution with 2 degrees of freedom.
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Recalculate according to your conditions!

Answer & Explanation

Jeroronryca

Jeroronryca

Expert

2022-07-20Added 13 answers

Suppose X 1 , , X n   i.i.d.   N ( μ , σ 2 ) and
X ¯ = X 1 + + X n n
and
S 2 = 1 n 1 ( ( X 1 X ¯ ) 2 + + ( X n X ¯ ) 2 ) .
Then
X ¯ μ σ / n N ( 0 , 1 )
and
X ¯ μ S / n t n 1 .
If you want 2 degrees of freedom, just use X 1 , X 2 , X 3 .

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Faith Welch

Faith Welch

Expert

2022-07-21Added 1 answers

How do you define t n distribution? By Z / χ n 2 / n where Z N ( 0 , 1 ) indept of χ n 2 .
Note, X i / i i i d N ( 1 , 1 ) or
Y i = X i i 1 i i d N ( 0 , 1 ) . Consider 2 Y 1 Y 2 2 + Y 3 2

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