Kindly help solve the following questions. Please show steps

(i) Write down a formula for F(ex ) where X - N(W,o') and, by differentiating, or otherwise, derive an expression for E (Xe ). [2] (ii) Show that: X, =(3, - atjean, ta's is a martingale, where B, is a standard Brownian motion, and a is an arbitrary constant. You may assume that E X,| . [5] [Total 7]Let B, (1 2 0 ) be a standard Brownian motion with B, =0. (i) By first writing down an expression for d( B), show that IB, dBy = 1(B -1) 14] (ii) What is the expected value at time 0 of B dB ? [2] (iii) What is the expected value at time a (0