Convergence in distribution of a random variable

This video explains what is meant by convergence in distribution of a random variable. Check out ben-lambert.com/econometrics-... for course materials, and information regarding updates on each of the courses. Quite excitingly (for me at least), I am about to publish a whole series of new videos on Bayesian statistics on youtube. See here for information: ben-lambert.com/bayesian/ Accompanying this series, there will be a book: www.amazon.co.uk/gp/product/1...

[@brandomiranda6703]

at around 3:28 ur sound disappears.

[@kiranbhattarai6755]

i think its on purpose.

[@DonArmadillo]

@@kiranbhattarai6755 I thought it was my PC bugging and restarted it haha

[@primingdotdev]

He got confused for a second. He was just making sure the math works out to check convergence in dist and but not in probability. Source: mind reading.

[@edwardw7965]

excellent explanation. The geographic meaning worth more than anything.

[@Mark-vr2nx]

Awesome explanation!

[@mosesloo9273]

you the real mvp

[@honcheunghui5684]

Just want to know how do we know the converge rate is sqrt of N?

[@jdm89s13]

When we say X_n converges in distribution to X, do we mean the summation of the random variables from X_1 to X_n is what's converging in distribution to X?
The way I always see it stated is that X_n itself converges in distribution to X, but why would the nth draw from a population have a different cdf from the first, second, or any other draw from the population?

[@naveenkartik1482]

X_n is a sequence of random variables.

[@ashishsinghalagarwal6561]

Consider X_1 to X_n as some random variable and then apply the above video concepts.

[@arkabose89]

it wont have different cdf. if u plot distribution of Y, it is going to be same as the one of x. hence convergence of distribution.

[@laodrofotic7713]

@@naveenkartik1482 yeah and the guy in the video didnt say that. Thats the definition of a bad teacher.

[@PF-vn4qz]

what is confusing though is what it means if Xn converges in distribution to a constant. I mean what is the cdf of a constant??

[@TheMrAineas1]

I’d guess that the cdf of a constant (let’s say c) would be zero for x=c since it is implied that P(X=c)=1

[@firdausfitri7806]

hi
how do you get the Y=1-X ?
thankyou

[@yrret1996]

i think he just defined it as a new rv

[@jankral7760]

since p=0.5 for both x=0,1: Pr(X=x)=0.5. Now Y=1-X, complement of X so, Pr(Y=x)=0.5 for both x=0,1. Looking up bernouli formula and making sure it makes sense help for the intuition :))

[@user-li5sq3up9h]

The sound of the videos is not good

[@jameswhite5293]

Normally love your videos, but this one is missing labels on the graph axis and that's a critical flow unless you know the labels :(