1. Questions

Probability

Bias and MSE

We estimate the unknown mean θ of a random variable X with unit variance by forming the sample mean Mn=(X1+⋯+Xn)/n of n i.i.d. samples Xi and then forming the estimator

Θˆn=13⋅Mn.

Your answers below can be functions of θ and n. Follow standard notation and use 'theta' to indicate θ.

The bias E[Θˆn]−θ of this estimator is:
unanswered

The mean squared error of this estimator is:
unanswered

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SK

  1. For biais: -2*theta/3

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    Meeto

  2. -2*theta/3

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    Cheat

  4. mse: 4*theta^2/9

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    Helper

  5. Helper's answer is kinda right, but input it like:
    (4*theta^2)/9

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    Hierarchy is important

  6. Actually above is just part of the answer, mse is 1/9+(4*theta^2)/9

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    alpha

  8. typo above: (1/9*n)+(4*theta^2)/9

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    alpha

  9. (1/(9*n))+(4*theta^2)/9

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    Humble1

  10. -2*theta/3

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    Anonymous

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