Suppose we generate n = 100 independent and identically distributed uniformly random numbers N1,..., Nn on...

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Suppose we generate n = 100 independent and identically distributed uniformly random numbers N1,..., Nn on the interval [0, 100]. Let N1,..., n be the rounded versions, where we either round up or down to the nearest integer. For instance N1 = 1 if N1 < 1.5 and N2 sum of the numbers and S = EL Ñ; the sum of the rounded numbers. Using the Central Limit Theorem, estimate the probability that |S - Ŝ| < 1. Use the value (V3/5) - 0.64 to simplify your final answer as much as possible. 17 if N2 > 16.5. Let S = D Ni be the :1 Hint: Consider the "round-offs" R; = N; - Ñ;. How are they distributed? Notice that S- Ŝ = E Ri- Suppose we generate n = 100 independent and identically distributed uniformly random numbers N1,..., Nn on the interval [0, 100]. Let N1,..., n be the rounded versions, where we either round up or down to the nearest integer. For instance N1 = 1 if N1 < 1.5 and N2 sum of the numbers and S = EL Ñ; the sum of the rounded numbers. Using the Central Limit Theorem, estimate the probability that |S - Ŝ| < 1. Use the value (V3/5) - 0.64 to simplify your final answer as much as possible. 17 if N2 > 16.5. Let S = D Ni be the :1 Hint: Consider the "round-offs" R; = N; - Ñ;. How are they distributed? Notice that S- Ŝ = E Ri-