Question: 4. (10 points) Let X1, X2, ..., Xn be i.i.d. random sample with finite mean /, let Y = > Xi and assume X; comes

4. (10 points) Let X1, X2, ..., Xn be i.i.d. random sample with finite mean /, let Y = > Xi and assume X; comes from Poisson distribution, then X = - is approximately N (, " ) Y for n n large n. Show that the variance Var does not depend on /. Hint: You will need delta theorem for this

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