Mean and variance of Binomial Distribution - A simple proof

For books, we may refer to these:

This lecture gives proof of the mean and Variance of Binomial distribution. Also, two examples are given to explain it.
Other distribution

[md.mahedihassanlemon]

Clear interpretation 😇...Take love❣️❣️ from Bangladesh 🇧🇩🇧🇩🇧🇩

[ovqgwtp]

In your previous video about Binomial distribution, for discrete it was probability density function and here you are mentioning about pmf. I m confused with pdf and pmf

[beenarai]

Easy and best way to teach thank you so much sir 😊

[liwen]

Hi sir, I just wanna ask when we prove Var(X), why cannot we directly use sum of x^2 *p -{E(X)}^2?But we need to write X^2 in X(X-1) form? Thx !❤❤

[tavleensasan]

Sir why E(X(X-1))=x.(x-1). P(x) why not E(X(X-1))=x(x-1).P(x(x-1)) in Variance derivation.

[poonambajaj]

In last example the mean(0.4) is not greater than variance(1.6) which is the resultant of relation between mean and variance of binomial distribution. Does it mean that the distribution or that example does not belong to binomial?

[Dupamine]

what does it even mean for something to be 'expected value of 5 or 6'?

[risahabhbeast]

Sir why did the domain change from 0 to 1 when we cancelled out x 1:36

[berealistic]

Plzzz let me know theirs proofs do come in