Binomial Distribution#

Motivation#

$Y = \begin{array}{ c l } 1 & \quad \textrm{with probability} p \\ 0 & \quad \textrm{with probability } 1 - p \end{array}$

TODO

Consider a random variable defined as the sum of n Bernoulli random variables,

$X = Y_1 + Y_2 + ... + Y_{n-1} + Y_n$

Where each $Y_i$ takes the value 1 with probabilitiy p or it takes the value 0 with probabilitiy 1 - p.

TODO

From Conditional Probability the probability of an intersection of independent events is the product of individual probabilitiy,

$P(A \cap B) = P(A) \cdot P(B)$

TODO

$p(x; n, p) = C^{n}_x \cdot p^{x} \cdot (1 - p)^{n-x}$