question
Question 1. Brownian bridge [12 marks] Consider the process where 𝐵𝑡 is a standard Brownian Motion. (a) Show that 𝑋𝑡 is a standard Brownian bridge [3 marks]. (b)Find 𝐸[exp(2𝑋1/2 − 4𝑋1/3)] [3 marks]. (c) Find 𝐸[𝑋1/4|𝐵5/6] [3 marks]. (d)Using the result from (c), use R or Mathematica to compute 𝑃 (14 < 𝐸[𝑋1/4|𝐵5/6] < 12). …