5.6 Computer quiz

1. If one single integration with 100 samples falls within 1% of the analytical value
   
   1. 10000 samples yield an error smaller than 0.01%
   2. 10000 samples yield an error around 0.1%
   3. 10000 samples yield an error that is likely to be larger than 0.1%

2. In a Wiener process, the increment immediately following an increment of 0.23 is
   
   1. likely to be negative rather than positive
   2. uniformly distributed in [-1;1]
   3. uniformly distributed in [0;1]
   4. independent of the past realisation

3. In a Brownian motion, the increment (mean free path) is
   
   1. propotional to the square-root of the diffusion coefficient
   2. propotional to the diffusion coefficient
   3. independent of the diffusion coefficient

4. The numerical error in our MCM scheme for advection-diffusion is
   
   1. proportional to the square-root of the time step
   2. proportional to the time step
   3. independent of the time step

5. Monte Carlo discretization of non-linear equations such as Burger's is
   
   1. impossible
   2. particularly slow
   3. difficult to parallelize

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