Convergence

Convergence in Probability[edit | edit source]

Consider a sequence of random variables and another random variable .

The sequence converges in probability to if

for every .

Convergence with Probability 1[edit | edit source]

Consider a sequence of random variables and another random variable .

The sequence converges with probability 1 to if

Suppose that a sequence is such that

then

Convergence in Distribution[edit | edit source]

Consider a sequence of random variables and another random variable .

The sequence converges in distribution to if

for every real value such that .

If then

If then

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