Roll a die independently 2000 times where the probability of getting a “1” is p. Let X be the total number of getting a “1” till time 2000. Let X ̄n = X/2000. 1.State the central limit theorem. 2.Using the notation Φ(x) = P(Z ≤ x), approximate P(300 ≤ X ̄n ≤ 400) when p = 1/6.

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Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.