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Proof the binomial MLE is unbiased

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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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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Easy_A
OP
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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Original post by Easy_A
Yeah that is what I mean, so thanks for clarifying that!


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No problem :smile:
Reply 4
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Easy_A
OP
Original post by Smaug123
No problem :smile:


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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