Probability Distributions: Apply It 2

  • Understand the concept of a probability distribution and its role in describing the behavior of a random variable.
  • Describe the characteristics of probability distributions.

Probability Distributions

Notice the following important facts about probability distributions:

  • The outcomes are random events.
  • All outcomes are assigned a probability.
  • The probabilities are numbers between [latex]0[/latex] and [latex]1[/latex]. This makes sense because each probability is a relative frequency.
  • The sum of all of the probabilities is [latex]1[/latex]. This makes sense because we have listed all the outcomes. Since each probability is a relative frequency, these outcomes make up [latex]100\%[/latex] of the observations.

It’s difficult to judge whether or not the spinner is fair based on only [latex]5[/latex] spins.

The Law of Large Numbers says that as we increase the number of times we repeat a chance experiment, the closer we can expect the empirical probability calculated from our chance experiment to be to the true probability.

The Law of Large Numbers tells us that as the number of trials gets really large, the simulated probability based on the chance experiment and the true probability of the chance experiment will approach the same value.

The law of large numbers does not mean that a given sample will always reflect the true characteristics, especially for small samples. Therefore, for our example, we cannot judge whether or not the spinner is fair based on only [latex]5[/latex] spins.