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# Bernoulli Distribution Basics

Created by
@DiligentTriumph

## Questions and Answers

### In a Bernoulli trial, what is the probability density function?

$f(x) = p^x(1-p)^{1-x}$

### What is the mean of a Bernoulli random variable?

$p$

### What does the variance of a Bernoulli random variable equal to?

$p(1-p)$

### What is the probability of getting a score less than 5 in a throw of a six-sided die?

<p>$2$</p> Signup and view all the answers

### What does the MGF of a Bernoulli random variable equal to?

<p>$M(t) = 1 - p + pe^t$</p> Signup and view all the answers

### An experiment with only two possible outcomes can be considered a Bernoulli trial.

<p>True</p> Signup and view all the answers

### The probability density function of a Bernoulli random variable is given by $f(x) = p^x(1-p)^{1-x}$, where $p$ is the probability of success.

<p>True</p> Signup and view all the answers

### The mean of a Bernoulli random variable is equal to its probability of success, $p$.

<p>True</p> Signup and view all the answers

### The variance of a Bernoulli random variable is given by $Var(X) = p(1-p)$.

<p>True</p> Signup and view all the answers

### The moment generating function of a Bernoulli random variable with probability of success $p$ is $M(t) = 1-p + pe^t$.

<p>False</p> Signup and view all the answers

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