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Probability: Difference between revisions
→In Distribution
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===In Distribution=== | ===In Distribution=== | ||
Pointwise convergence of the cdf<br> | Pointwise convergence of the cdf<br> | ||
A sequence of random variables <math>X_1,...</math> converges to <math>X | A sequence of random variables <math>X_1,...</math> converges to <math>X</math> in probability | ||
if for all <math>x \in S</math>, | if for all <math>x \in S</math>,<br> | ||
<math>\lim_{i \rightarrow \infty} F_i(x) = F | <math>\lim_{i \rightarrow \infty} F_i(x) = F(x)</math> | ||
* Equivalent to convergence in probability if it converges to a degenerate distribution | * Equivalent to convergence in probability if it converges to a degenerate distribution | ||