Section 4: Bivariate Distributions

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In the previous two sections, Discrete Distributions and Continuous Distributions, we explored probability distributions of one random variable, say X. In this section, we'll extend many of the definitions and concepts that we learned there to the case in which we have two random variables, say X and Y. More specifically, we will:

  • extend the definition of a probability distribution of one random variable to the joint probability distribution of two random variables
  • learn how to use the correlation coefficient as a way of quantifying the extent two which two random variables are linearly related
  • extend the definition of the conditional probability of events in order to find the conditional probability distribution of a random variable X given that Y has occurred
  • investigate a particular joint probability distribution, namely the bivariate normal distribution