## Probability sheet 4

Here is a sketch of problem 10 on sheet 4. The convergence question that came up in the tutorial is clarified in an elementary way.

Added: Towards the end of the document, I should have stated that $S_N$ is a Riemann sum for the integral with mesh size $2^{-N+1}$, Since this goes to zero and we are integrating a continuous function, we get convergence of the sum to the integral.