answer all questions with explanation

Q4. (a) Consider the sample space $2 of three coin tosses. Let So =4;u=2;d =1/2; p= 2/3. Compute EI [S1 S3|w1 = H]. (7 marks) (b) In a European call option, consider a function f defined by f (x) = E(S2|$3 = x). Find the maximum number of elements in range(f). (3 marks) (c) In a symmetric Random walk (My), prove that var(M,) = n. (15 marks) [Total : 25 marks]