Expected Value, Mean, Variance, Standard Deviation

[@gimliofdurin]

Great summarization of these concepts! Thanks, really appreciate you putting this video up.

[@Moshietv]

That moment when hes like like pull out the 2 and the mew and u expected him to say mewtwo lool

[@TheBazama]

Thank you for the great presentation, it really helped me
In the last example;I think f(4) should be equal to 8/81,
Suppose P=1/3 denote the probability of rolling 5 or 6, then (1-P) is the probability for any of the others each time you throw a die which is 2/3.
thus f(4)=P(1-P)^3 such as f(x)=P(1-P)^(x-1).
therefore:
f(1)=P(1-P)^0=(1/3)(2/3)^0=1/3
f(2)=P(1-P)^1=(1/3)(2/3)^1=2/9.
f(3)=P(1-P)^2=(1/3)(2/3)^2=(1/3)(4/9)=4/27.
f(4)=P(1-P)^3=(1/3)(2/3)^3=(1/3)(8/27)=8/81.

[@FernandoLopez-rd8jv]

in the last problem why is the probability of getting 5 or 6 equal to 2/9 when rolling the dice the second time?

[@dmsayim]

I think in the vriance slide (in note line no-1 there would be square over the first bracket

[@hannahmctigue9616]

The last thing you say is, "The variance will be the square root of that number," but you mean that the standard deviation is the square root of "that number" (variance)

[@thegrisha]

Very helpful, thank you very much.

[@paridhisharma3896]

plz explain the how you take prob.of f(1),f(2),f(3) and f(4) in the last question

[@shroukel-attar5859]

Perfect, thank you!

[@thragg00]

Thanks for this

[@hannahmctigue9616]

probability for 1st roll is 4/6, since you did not roll a 5 or 6. probability for 2nd roll is 2/6, since you did roll a 5 or 6, thus causing you not to roll a 3rd time. probability of 2 rolls=4/6*2/6=2/9

[@herbertjosephy2397]

Thank u sir