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1. Let X1, X2,... be independent random variables each with the standard normal distribution, and for each n 0 let Sn 너 1 i. Use importance sampling to obtain good estimates for each of the following probabilities: (a) P[maxns 100 Sn > 10); and (b) P[maxns100 Sn > 30 HINTS: The basic identity of importance sampling implies that n100 where Po is the probability measure under which the random variables Xi, X2,... are independent normals with mean 0 amd variance 1. The identity is valid for any choice of 6, but you will find it best to try the value θ-K/100.

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1. Let X1, X2,... be independent random variables each with the standard normal distribution, and for...
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