Random Variables and Distributions in Data Science
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Questions and Answers

What is the definition of joint probability according to the text?

  • The probability of an event irrespective of the other variables.
  • The probability of one variable being dependent on a second variable.
  • The probability of simultaneous events, such as the outcomes of two different random variables. (correct)
  • The probability of an output given an input example.

What is the relationship between joint probability and the 'fundamental rule of probability' or 'product rule' or 'chain rule' of probability?

  • The fundamental rule/product rule/chain rule is used to calculate joint probability. (correct)
  • Joint probability is a subset of the fundamental rule/product rule/chain rule.
  • They are all different names for the same concept.
  • The fundamental rule/product rule/chain rule is a consequence of joint probability.

What is the definition of marginal probability according to the text?

  • The probability of simultaneous events, such as the outcomes of two different random variables.
  • The probability of an event irrespective of the other variables. (correct)
  • The probability of one variable being dependent on a second variable.
  • The probability of an output given an input example.

In the example provided, what does P(city1 city2) represent?

<p>The probability of any weather event occurring in both City-1 and City-2. (A)</p> Signup and view all the answers

What is the definition of independence or statistical independence according to the text?

<p>When one variable is not dependent on a second variable. (C)</p> Signup and view all the answers

Which of the following statements about joint probability and marginal probability is true?

<p>Marginal probability is a special case of joint probability. (D)</p> Signup and view all the answers

In the example provided, what does P(city1=sunny city2=sunny) represent?

<p>The joint probability of a sunny day in both City-1 and City-2. (A)</p> Signup and view all the answers

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