MCS: discrete random variable Bernoulli distribution

Bernoulli

$x$ Is Bernoulli variable , The value is 0/1:
$$P(x=1)=p$$
$$p(x=0)=1-p$$

Expectation and variance ：

$$E(x)=p$$
$$V(x)=p(1-p)$$

The generation process of random Bernoulli variables is as follows ：

1. Generate a random uniform variable $u\sim U(0,1)$
2. if $u<p,x=1;else,x=0$

example ： Set a Bernoulli variable $x$,$p(x=1)=0.7$, The random Bernoulli variables are generated as follows ：

1. Generate a random variable $u=0.5$
2. $u<p(x=1),x=1$