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

Definition. Xn → X in probability if
 for every > 0,

Let F1, F2, . . . and F be the distribution functions of X1, X2, . . . and X respectively.
Definition. Xn → X in distribution (or weakly), if
 for every x such that F is continuous at x,

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


what is the uniqueness theorem for PGFs


uniqueness theorem (for MGFs)

continuity theorem (for MGFs)

what is the characteristic function

