Probability Distributions & Descriptive Statistics - Bernouilli and Binomial Distribution

10 important questions on Probability Distributions & Descriptive Statistics - Bernouilli and Binomial Distribution

1. What is a Bernoulli distribution?

A Bernoulli random variable has only two possible outcomes:
success (coded as 1)
failure (coded as 0)
It models a single trial of an experiment.

2. What are the key parameters of a Bernoulli variable?

  • p = P(success)
  • 1 − p = P(failure)
  • What is the expected value (mean) of a Bernoulli variable?

    E(X) = p
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    What is the variance of a Bernoulli variable?

    Var(X) = p(1 − p)

    What is a Binomial distribution?

    A Binomial distribution models the number of successes in n independent Bernoulli trials with the same probability p.

    What are the parameters of a Binomial variable?

  • N = number of trials
    P = probability of succes in each trial

    X ∼ Bin(n, p)
  • What is the probability mass function (PMF) of a Binomial variable?

    Formula:

    What is the mean of a Binomial distribution?

    E(X) = n x p

    What is the variance of a Binomial distribution?

    Var(X) = n x p x (1 - p)

    Relationship between Bernoulli and Binomial

    Bernoulli = 1 trial
    Binomial = sum of several Bernoulli trials

    The question on the page originate from the summary of the following study material:

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