Bernoulli Distribution Basics
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Questions and Answers

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

  • $f(x) = p^x(1-p)^{1-x}$ (correct)
  • $f(x) = p+x(1-p)$
  • $f(x) = p^2(1-p)^2$
  • $f(x) = p(1-p)$

    • What is the mean of a Bernoulli random variable?

  • $1-p$
  • $p^2(1-p)^2$
  • $p$ (correct)
  • $p(1-p)$

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

  • $p^2(1-p)^2$
  • $p(1-p)$ (correct)
  • $p$
  • $(1-p)$

    • 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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