Unit 7: Random Variables and their PDFs

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Connections

Probability
  • This unit centers around probability and, like the previous unit, it stresses the importance of how the probabilities associated with values in a random experiment (which we model using pdfs in this unit) differ from the relative frequencies of values found within populations (which we’ve modeled using mathematical functions in previous units).

  • Simulating probabilities is also a very powerful tool and is referenced briefly in this unit. The following unit will expand more on this topic.
Models
  • Many probability models are referenced in this unit, but a lot of the examples you might use will refer back to the normal model in particular. This model will continuously be referenced in future units.

  • As discussed in earlier units, one can identify what distribution is appropriate to model a situation by describing distributional characteristics such as the shape, center and spread.
Inference
  • As referenced in the previous unit, modeling probabilities is a key piece to statistical inference to determine whether a sample statistic is typical or unusual under the assumption of a particular model. This unit attempts to make this connection more clear and in future units, this point will be even more explicit.