Probability

Let
Yn=∑i=1n(−1)iXi=−X1+X2−X3+⋯,

where the Xi are i.i.d., with E[Xi]=0, and var(Xi)=4.

Is
1nYn

approximately normal? Choose the most appropriate response:

No.

Yes, because the {Yi}i=1∞ are i.i.d., so we can directly apply the Central Limit Theorem.

Yes, because the {(−1)iXi} are i.i.d., so we can directly apply the Central Limit Theorem.

Yes, because Yn/n is the sum of two independent approximately normal random variables.

Yes, because E[Yi]=0 and var(Yi) is finite, so we can directly apply the Weak Law of Large Numbers.

(i)
(ii)
(iii)
(iv)
(v)
unanswered

Find the variance of Yn.

var(Yn)= unanswered

Find P(Y100≥20), approximately.

P(Y100≥20)≈ unanswered

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