Part A Probability

Definition. Xn → X almost surely (or “with probability 1”) if

Definition. Xn → X in probability if

Let F1, F2, . . . and F be the distribution functions of X1, X2, . . . and X respectively.
Definition. Xn → X in distribution (or weakly), if

which modes of convergence imply which other modes of convergence

state the weak law of large numbers

state markov's inequality

state chebyshev's inequality

state the strong law of large numbers

state the central limit theorem

define PGF

what is the uniqueness theorem for PGFs

what is an MGF

uniqueness theorem (for MGFs)

continuity theorem (for MGFs)

what is the characteristic function