Assume a time series with the following distribution.

St= St-1+(-1)t ∗ U

where U is a random variable with Uniform (0,a) distribution.

a) Derive a generalized solution to calculate probability of St > K

b) Given S0=1000 & a = 1, calculate the Probability of S50 > 1002

c) Confirm your answer for (b) using Monte-Carlo simulations. Please attach your script.