Critical limit theorem

Any help for Q !,2 would be appreciated

Any help for Q !,2 would be appreciated

I haven't worked these through, but a couple of points:

1.

X_n \sim N(\mu,\sigma) \Rightarrow X=\frac{1}{144}(X_1 + \cdots + X_{144}) \sim N(\mu, \frac{\sigma^2}{144})

by the Central Limit Theorem and expectation algebra.

2.

X \sim N(0,1) \Rightarrow X^2 \sim \chi_1^2

so adapt this for

X \sim N(0,3)

then use the Central Limit Theorem.

I haven't worked these through, but a couple of points:

1.

X_n \sim N(\mu,\sigma) \Rightarrow X=\frac{1}{144}(X_1 + \cdots + X_{144}) \sim N(\mu, \frac{\sigma^2}{144})

by the Central Limit Theorem and expectation algebra.

2.

X \sim N(0,1) \Rightarrow X^2 \sim \chi_1^2

so adapt this for

X \sim N(0,3)

then use the Central Limit Theorem.

thanks for the points but i'm still clueless

thanks for the points but i'm still clueless

Could you expand on the precise extent of your cluelessness? What didn't you follow?

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