It is widely believed that the daily change in currency exchange rates is a random variable with mean 0 and variance v
That is, if Yn represents the exchange rate on the nth day, Yn = Yn−1 + Xn, n = 1, 2, . . . where X1,X2, . . . are independent and identicallydistributed normal random variables with mean 0 and variance v. Suppose that today’s exchange rate is 1.55 and v = 0.0025, then what is the probability that the exchange rate will be below 1.4 in 9 days and in 25 days?
Am I meant to setup a diffferential equation, I'm not sure?