Suppose {X,n} is a sequence of random variables draw from an underlying popu- lation space, then the sample mean of {Xn} defined as Xn = i-1Xi, converge in distribution to Normal Distribution N(u, o2), where u = E[X;], o2 Var[X 11 n (a) Randomly draw 10000000 samples from from N(20,25), plot the histogram of the samples and underlying population distribution together

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A: The problem can be solved using the concept of expectation and moment generating function.

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A: Please see the handwritten solution.

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A: Result: if X~χ2(n) Mx(t)=(1-2t)-n/2 If X and Y are independent then E(XY)=E(X)E(Y)

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A: Given: confidence level = 0.95 Margin of error E = σ4 Formula Used: n = Zα/2×σE2