1. If X1, X2, X3, X4 are a random samle from a normal distribution with mean 17, then what is the distribution of [itex]2(X - 10) / S[/itex] where X should be X bar.(adsbygoogle = window.adsbygoogle || []).push({});

Our notes are just awful for this topic.

Any tips how to proceed with this one, and what is S?

2. Let X1, X2, ... be a sequence of independant and identically distributed random variables with mean zero and variance 36. What is the sequece Cn for which

lim p -> inf [itex] P ( (X / Cn) \leq x) = P (Z \leq x), Z ~ N(0,1) ?[/itex]

Would this just be sqrt(Var) = sqrt(36) = 6 ?

4. What is the distribution of X/Y where X and Y are independant [itex]{X^{2}}_{1}[/itex] random variables? (chi-squared with 1 deg. of freedom)

Not sure how to progress with this one, do we play with the degrees of freedom to get some sort of trivial answer?

5. Is theta-hat consistent if MSE(theta-hat) = [itex]e^{1/n} -1[/itex].

Since MSE approaches 0 as n approaches infinity (n-> inf, MSE -> [itex]e^{0} -1[/itex] -> 0) then yes, theta-hat is consistent. ?

Thanks for your time

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# Statistical 'Inference'

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