binomial distribution

a probability distribution the probability of a specific incident to occur $\text{[math]}$ times out of $\text{[math]}$ times is a combination, so: $\text{[math]}$ such that $\text{[math]}$ , $\text{[math]}$

a random variable is binomially distributive with the parameters $\text{[math]}$ and is written as $\text{[math]}$ if $\text{[math]}$ receives the values $\text{[math]}$ with the probabilities $\text{[math]}$ (the formula above)

the symbol of the binomial distribution is $\text{[math]}$
expected value is $\text{[math]}$
variance is $\text{[math]}$

bernoulli trial

independent repeated trials of an experiment with exactly two possible outcomes are called bernoulli trials

if $\text{[math]}$ then $\text{[math]}$