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

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Statistical 'Inference'

**Physics Forums | Science Articles, Homework Help, Discussion**