Binomial distribution

Binomial distribution is a bernoulli distribution in an experiment which is repeated n times (usually to find the probability of x ocurrences in n experiments).

Probability Mass Function:



Median:

np

Mode:

(n+1)p

variance:

np(1-p)


Example:

In a game a player trhow the dice 10th times hoping to get the 6 numbers  three times in order to win a prize. Define the median, mode, variance and probability to win the game.

Median:

(10)*(1/6) = 1.67

Mode:

(10 + 1)*(1/6) = 1.83

Variance:

10*(1/6)*(5/6) = 1.389

Probability:

(10|3)*(1/6)^3*(5/6)^7 =  0.155