Generate a sequence U1,U2, . . . ,U1000 of independent
Chapter , Problem 30(choose chapter or problem)
Generate a sequence \(U_{1}, U_{2}, \ldots, U_{1000}\) of independent uniform random variables on a computer. Let \(S_{n}=\sum_{i=1}^{n} U_{i}\) for n = 1, 2, . . . , 1000. Plot each of the following versus n:
a. Sn
b. \(S_{n} / n\)
c. \(S_{n}-n / 2\)
d. \(\left(S_{n}-n / 2\right) / n\)
e. \(\left(S_{n}-n / 2\right) / \sqrt{n}\)
Explain the shapes of the resulting graphs using the concepts of this chapter.
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