Sample Function

• first argument is c(), which contains the outcomes
• second argument is size=, which contains the number of simulations
• third argument is replace=, which specifies whether replacement occurs
• fourth argument is prob=c(), which contains the likelihood of each outcome

Binomial Random Variable

the number of successes in $n$ independent success/failure trials

Two Parameters:

• $n$ = the number of trials
• $p$ = the probability of success on each trial

Equation:

$P(X = x) = \binom{n}{x}\space p^x \space (1-p)^{n-x}$ for $x \in \{0,1,2, …, n\}$

• $\binom{n}{x}$

$X$~ Binomial$(n,p)$

• Mean/Expected Value $E[X] = \mu = np$
• Variance $Var(X) = \sigma^2 = np(1 - p)$
• Standard Deivation $SD(X) = \sigma = \sqrt{np(1-p)}$
• example

dbinom Function