Example of Probability Density Function (PDF)

The coach of a baseball team wants to know the probability that a particular player hits one home run during a game where the player goes up to bat 4 times. Based on the player's past games, the coach assumes that the player has a 0.10 probability of hitting a home run in the current game. Because the player will either hit a home run or he will not for each time at bat, the coach uses the binomial distribution.

Note

This example uses the binomial distribution; however, this method is similar for any distribution that you select.

  1. In an empty worksheet column, such as C1, type 0, 1, 2, 3, and 4 into separate rows. These values represent the number of home runs that the player could hit over the duration of the game.
  2. Open the Probability Density Function (PDF) dialog box.
    • Mac: Statistics > Probability Distributions > Probability Density Function
    • PC: STATISTICS > CDF/PDF > Probability Density Function
  3. From Form of input, select A column of values.
  4. From Values in, select C1.
  5. From Distribution, select Binomial.
  6. In Number of trials, enter 4.
  7. In Event probability, enter 0.1.
  8. Under Output, select Display a table of cumulative probabilities. If you prefer to store the values in the worksheet, select Store cumulative probabilities in a column.
  9. Click OK.

Interpret the results

The probability that the baseball player will hit one home run over 4 attempts is 0.2916. The probability that the player does not hit a home run during the game is 0.6561. The probabilities of hitting more than one home run during the game are much smaller. For example, the probability that the player will hit a home run each of the 4 times he bats is 0.0001.

Summary
Input
Number of trials
Event probability
Probability Density
x
P(X = x)
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