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Thread: Unbiased Estimator Question

  1. #16
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    Re: Unbiased Estimator Question




    Well keep working at it. Try combining like terms. Use the fact that a^cb^c = (ab)^c to combine some like terms.

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    Re: Unbiased Estimator Question

    so now I have exp(-3*lambda)*summation(((-2)^y)*exp(2*lambda)*lambda^y/y!)... so if I combine the first and the last I have (inside the summation) exp(2*lambda)*-2lambda^y/y!... I'm not sure how to get rid of the extra factors

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    Re: Unbiased Estimator Question

    Try the substitution K = -2\lambda. Does the inside of the summation look somewhat familiar now?

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    Re: Unbiased Estimator Question

    OH!!! Oh my gosh, can't believe I missed that. I thought I needed to do a substitution but it was all too foggy I guess... yay!!! Thank you!!

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    Re: Unbiased Estimator Question


    No problem. Just one thing you should probably be careful about though - you don't want to claim that the summation is 1 because the inside is the pmf of a poisson. Because technically it isn't. What are the restrictions on \lambda for a poisson? Does your summation meet those restrictions? Nope. But that still does sum to 1. If you know the taylor series expansion of e^x you should be able to show this.

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