1. Consider a stock Ssuch that dS = m S dt + s S dz, and let r be the risk-free interest rate. Assume that r is constant. The stock is worth S₀ Euros today and does not pay dividends. Let T be a fixed maturity.
   1. Calculate the expected value and the variance of S_T under the risk-neutral probability using the following result: if U ~ f(0,1) is a centred Gaussian random variable, E[exp(aU)] = exp(a²/2) for any constant a.

(p.s values are not given so the answer should be provided with variables)