9.2. Sampling bias la Cameron-Martin. We consider a Brownian motion with drift 0 = 1: B...

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9.2. Sampling bias la Cameron-Martin. We consider a Brownian motion with drift 0 = 1: B = B+t. (a) Generate a sample S of 100,000 paths for (B, t = [0,1]) using a 0.01 dis- cretization. (b) Using the function numpy.random. choice, sample 1,000 paths in S not uni- formly but proportionally to their weight: M(B) = e-B+1/2 Again you will need to normalize the weights M(B) so that the sum over the 100,000 paths is 1. Let's call this new sample S. (c) Draw the histogram of B/2 on the sample 5. It should look like a Gaussian PDF with mean 0 and variance 1/2. 9.2. Sampling bias la Cameron-Martin. We consider a Brownian motion with drift 0 = 1: B = B+t. (a) Generate a sample S of 100,000 paths for (B, t = [0,1]) using a 0.01 dis- cretization. (b) Using the function numpy.random. choice, sample 1,000 paths in S not uni- formly but proportionally to their weight: M(B) = e-B+1/2 Again you will need to normalize the weights M(B) so that the sum over the 100,000 paths is 1. Let's call this new sample S. (c) Draw the histogram of B/2 on the sample 5. It should look like a Gaussian PDF with mean 0 and variance 1/2.