Why would T=XY+Z not be a sufficient statistic for X,Y,Zāˆ¼_(i.i.d) Bern(p)

pin1ta4r3k7b

pin1ta4r3k7b

Answered question

2022-11-17

Why would T = X Y + Z not be a sufficient statistic for X , Y , Z āˆ¼ i . i . d B e r n ( p )

Answer & Explanation

Zoey Benitez

Zoey Benitez

Beginner2022-11-18Added 18 answers

The function F is by definition a function of two variables x and y. It is trivial that we can take two partial derivatives of it.
This F implicitly defines a function f ( x ) of one variable by the constraint F ( x , y ) = c where š‘ is a constant.
The correct equation for f ā€² ( x ) you obtain from the chain rule:
d d x F ( x , f ( x ) ) = āˆ‚ āˆ‚ x F ( x , f ( x ) ) + āˆ‚ āˆ‚ y F ( x , f ( x ) ) f ā€² ( x ) .
Now observe that the LHS of this is zero because we said F ( x , f ( x ) ) is constant. Can you solve this equation now for
f ā€² ( x ) = d y d x ?

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