Bernoulli Trials

• Bernoulli Trials

 

A random experiments with exactly two outcomes. A real-life example of a Bernoulli trial is whether it will rain today or not. Now, the only possible outcomes are Yes and No and are independent of each other. Generally, the outcomes of a Bernoulli trial are success and failure.

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$$\begin{array}{}& X\sim <!--\; \sim \; -->\text{Bern}(x;\mathrm{\mu <!--\; \mu \; -->})\end{array}$$

 

- 𝑋 : A Random Variable

- ~ : Follow

- μ : The probability of get 1

 

$$\begin{array}{r}\begin{array}{}& \text{Bern}(x;\mathrm{\mu <!--\; \mu \; -->})=\{\begin{array}{ll}\mathrm{\mu <!--\; \mu \; -->}& \text{if }x=1,\\ 1-<!--\; -\; -->\mathrm{\mu <!--\; \mu \; -->}& \text{if }x=0\end{array}\end{array}\end{array}$$

 

is same as

$$\begin{array}{}& \text{Bern}(x;\mathrm{\mu <!--\; \mu \; -->})={\mathrm{\mu <!--\; \mu \; -->}}^x(1-<!--\; -\; -->\mathrm{\mu <!--\; \mu \; -->}{)}^{(1-<!--\; -\; -->x)}\end{array}$$

 

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