# Proof the binomial MLE is unbiased

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#1
Hi there,

Was just wondering if anyone could clarify this for me:

E[Phat]=E[(1/n)∑xi]=(1/n)∑E[xi]=(1/n)∑np=(1/n)n²p=np
Therefore E[Phat]=np so is unbiased

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5 years ago
#2
(Original post by Easy_A)
Hi there,

Was just wondering if anyone could clarify this for me:

E[Phat]=E[(1/n)∑xi]=(1/n)∑E[xi]=(1/n)∑np=(1/n)n²p=np
Therefore E[Phat]=np so is unbiased

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What exactly do you need to be clarified? "Unbiased" iff "estimate of the mean has expectation equal to the distribution mean", and you've just shown that.
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#3
(Original post by Smaug123)
What exactly do you need to be clarified? "Unbiased" iff "estimate of the mean has expectation equal to the distribution mean", and you've just shown that.
Yeah that is what I mean, so thanks for clarifying that!

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5 years ago
#4
(Original post by Easy_A)
Yeah that is what I mean, so thanks for clarifying that!

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No problem
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#5
(Original post by Smaug123)
No problem
Also, would the mle bias proof for gamma be like this:

E[Bhat]=E[(1/n*a)∑xi]=(1/n*a)∑E[xi]=(1/n*a)∑aB=(1/n*a)n*a*B=B

Therefore E[Bhat] ≠ Ba so is biased

Or have I done something wrong?

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