Mean and variance of Binomial Distribution - A simple proof

For books, we may refer to these:
amzn.to/34YNs3W OR amzn.to/3x6ufcE
This lecture gives proof of the mean and Variance of Binomial distribution. Also, two examples are given to explain it.
Other distribution
Mean and Variance of Binomial Distribution: • Mean and variance of B...
Binomial Distribution: • Binomial Distribution
Poisson Distribution (Part 2): • Poisson Distribution
Poisson Distribution (Part 1): • Poisson Distribution S...
Geometric Distribution: • Geometric Distribution...
Negative Distribution: • Negative Binomial Dist...
Uniform Distribution: • Uniform Distribution
Exponential Distribution: • Exponential Distributi...
Normal Distribution: • Normal Distribution: H...

[@md.mahedihassanlemon954]

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

[@JEE-nf1cv]

Clear explanation thank you very much

[@user-ov7qg2wt6p]

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

[@DrHarishGarg]

No problem its name only. ... In general, pmf is used for discrete distribution while pdf for continuous one...

[@misstopper1]

Thank you sir

[@tavleensasan2408]

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.

[@liwen9244]

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 !❤❤

[@kuldeepkonwar2195]

Derivation becomes difficult other way.

[@beenarai5273]

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

[@DrHarishGarg]

So nice of you.... Thanks

[@risahabhbeast7370]

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

[@endoumamoru3835]

If you put 0 in denominator, you will get (-1)!

[@DrHarishGarg]

When we cancel x it means x=0 exclude from the domain , thats why x change from 0 to 1.... Similarly for variance, we cancel x(x-1) thus x change from 0 to 2... Hope it clear.

[@AniketGupta-gn2we]

Thank u very much

[@poonambajaj17]

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?

[@DrHarishGarg]

Yes, when mean < variance for a random variable X then it means that X does not follow Binomial distribution.,

[@Dupamine]

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

[@DrHarishGarg]

Probability of 5or 6 is 1/6+1/6= 1/3..
Based on number of dice thrown, you can find the expected value as n*(1/3) =n/3

[@Dupamine]

@@DrHarishGarg Thank you Dr. harish . me and my friend watch your videos everyday. I understood the math behind this in the video but i am confused on what does 'expected value' conceptually mean in the case of dice. Usually it means the 'mean' but 'mean' makes less CONCEPTUAL sense when thinking of throwing dices.

[@berealistic4658]

Plzzz let me know theirs proofs do come in exams????????

[@DrHarishGarg]

Yes

[@shivanikumari6778]

Thanku sir 😊

[@harsh15ish]

machaya boss

[@shaik.......mini....3187]

Cool

[@MuhammadmustaphaZanna-ov8cw]

Sir please

[@socialmedia3167]

how q come? 2/3

[@endoumamoru3835]

q = 1 - p
So, 1-(1/3 )= 2/3

[@MdZiyaurrahman_123]

P kha se aa gya

[@vinitagnyanasuntharam1736]

Thanks sir