Answer by leonbloy for Quickly calculate the probability of 12 dice having...
You have $E[x]= 3.5$ and $ \sigma_x^2 \approx 3 $. Then $E[Z]= 42$ , $ \sigma_Z^2 \approx 36 $, $ \sigma_Z \approx 6 $By Chebyshev's inequality (one sided) $$P(Z<30) \approx P(\mu -Z \ge 12 ) =...
View ArticleAnswer by Not a Salmon Fish for Quickly calculate the probability of 12 dice...
I read that you are looking for easier method , so the suggestion is to use generating functions .We know that the die (standard) can have only the values of $1,2,3,4,5,6$. Then , the generating...
View ArticleAnswer by Eric for Quickly calculate the probability of 12 dice having sum...
Well, your approximation is correct though you can do things in a quicker way without requiring paper. One fact is that the variance of a uniform variable interval of length $L$ is $L^2/12$, so it’s a...
View ArticleQuickly calculate the probability of 12 dice having sum less than 30
I try to quickly answer the question of whether one should play a game: roll 12 fair dice and sum up the face values; if the sum is less than 30, win 10 dollars, otherwise lose 1 dollar.Let...
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