Convergence of random variables

This lesson (Lecture 4 from the Stochastic Processes course at Claremont McKenna College) covers the definitions of convergence with probability 1 and convergence in probability. It also includes an example of a sequence that converges in probability, but not with probability 1.

[@starklitho3456]

Thank you so much for the explanation! The example is excellent!! Wondering why so few likes for such a good video. I've been thinking about the difference of these convergence for a week and you save my world!! Thank you!

[@shuier525]

This is the best lecture I have had on this topic.

[@chaoviteliang8813]

This is an excellent explanation with a lot of insights!

[@orhanbugur5571]

Best video on this topic!

[@austinbristow5716]

Wouldn't the probability of C_4=0 be 1-1/4=3/4?

[@MarkHuberDataScience]

Hi Austin, thanks for watching! In that second line there, I'm writing the probability that C_i = 1, ignoring what the actual value was in the instance. So I wrote 1 / 4 below C_4 and the 0 to indicate that P(C_4 = 1) = 1 / 4. You are absolutely correct, P(C_4 = 0) = 1 - 1 / 4 = 3 / 4.