The promises and pitfalls of randomization in sequence prediction $(25$ points$).$ We have learned in class that the weighted majority algorithm $($WMA$)$ and the randomized weighted majority algorithm $($R$-$WMA$)$ share some key similarities: both of them place weights on experts that become lower as experts make more inaccurate forecasts. The key difference arises in how the algorithms aggregate the weights to make a prediction: while WMA deterministically goes with the majority vote, RWMA randomizes its prediction proportional to the weight on each expert. In this problem, you will