What is a random variable?

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[arvindkumarsoundarrajan]

The content is awesome. My humble suggestion is it will be nice while explaining the key concept keep it little bit slow. So our neurons can grasp it easier. The video is having the same speed throughout. Give pauses here and there!!!

[christophersoo]

random variable is similar to an event, but it gives you a numerical representation of it. For example:

let X denote the result from flipping a coin

here the "variable" it self could be Heads or Tails, but the numerical representation would be 0 or 1.

So what is the difference between a random variable and a pmf/pdf?

a pmf/pdf is a function that models a distribution. And multiple random variables can follow the same distribution, hence have the same pmf/pdfs. random variables are case specific, but pmf/pdfs are more generaly, and multiple random variables can have the same pmf/pdf

for example:

the number of heads you get when you flip a coin is a discrete random variable X

the number of votes candidate A gets during an election is a discrete random variable Y.

X and Y are not the same

but X and Y have the same pmf, they both follow the binomial distribution

[TheMechanicalLemon]

Not all random variables have pdfs tho.