Question 1-5 please

Introduction to Stochastic Processes, Assigment 2 0.1. Consider a log-normal random variable S = es+2, with Z ~ Norm(0, 1). Find the formula for the following expected values: 1. Ellis>ky], where K is a real positive constant and I is identity function; 2. E[SI(S>K)] 0.2. Let B(t) and W(t) be two independent Brownian motions. Show that X(t) = (B(t) + W(t))/v2 is also a Brownian motion. Find correlation between B(t) and X (t) 0.3. Let B(t) be a Brownian motion and 0