HOMEWORKS n. ! ( dead line march 24 )
1) Review and prove the continuity property of a probability measure.
2) Prove the elementary formula for the expectation of a random variable with a finite number of possible values.
3)Prove the Borel Cantelli lemma.
4) Review the general definition of a multinormal random variable. Prove that if B is a one-dimensional Brownian Motion, then the vector (B(s), B(t)), with t different from s, has a bidimensional normal distribution and write the expression of its density.
5) Ex 2.8 a) and c)
6 ) Exercices 2.12, 2.13, 2.15, 2.16
7) Calculate the quadratic variation of a B.M..
8) Ex. 2.18.
