Chapter 7.3, Problem 9E

QIA Let F-4c24, countible or, A, countible), show that is o-algebra. B Let (Fne N) is family of a-algebra on 2, prove that F. o-algebra Q2: Prove that: 1. X, is martingale -esin 2. M, -e sin B,, is martingale by using Ito formula Q3: A Let X, has stochastic differential with drift p(x)=-bx + c, and diffusion o²(x)=4x, let Y√X,, where X, ≥0, find dr B: Let X, -(-s), Ito integral process, find dx, and [x.xko). Q4: Let Y, =[x,dB, is Ito integral, such that X, is nonrandom process, find: التوزيع 1. The distribution of Y 2. The moment generating function of Y,.

Solve the following Probability Problem (solve all parts)   HW 2.x. (Headless Hunt)The Headless Hunt is an organization of 88 Hogwarts ghosts so elite thateven Nearly Headless Nick was annually denied admission for decades,despite being The Gryffindor ghost. The ghosts love playing sports anddecided to get together and have either a Head Polo tournament or aHorseback Head-Juggling tournament. However, even if they are ghosts,they still have jobs so some of them might have an urgent haunting as-signment. In order for no one to be left behind they need to be able tosplit into teams of equal numbers. Head polo teams consist of 4 playerswhereas Horseback Head-Juggling teams have 11 players. Assume thatany number of them from 1 to 88 show up with equal probability. a) What is the probability they will be able to play one of the twotournaments?b) If in addition to the previous 2 sports there was one more option, atournament in Headless bowling which is played in teams of 8 players,what would…

42. Consider the following joint probability table. B₁ B2 B3 B4 A 0.09 0.22 0.15 0.20 A 0.03 0.10 0.09 0.12