Statistical Applets The Law Of Large Numbers

Observe a random variable x very many times. In the long run, the proportion of outcomes taking any value gets close to the probability of that value. The Law of Large Numbers says that the average of the observed values gets close to the mean μ_x of x. In this applet, we represent a random variable x as the total number of spots on the "up" faces of one or more dice.	Choose the number of dice by clicking FEWER DICE or MORE DICE. To see the roll totals or the population mean number of spots μ_x, check the corresponding box at the left. Fill in the number of rolls you'd like to make and click ROLL DICE. The graph shows the average x of the spots for all of your rolls. As you make more and more rolls, x should eventually get close to μ_x.

Statistical Applets

The Law Of Large Numbers

Observe a random variable x very many times. In the long run, the proportion of outcomes taking any value gets close to the probability of that value. The Law of Large Numbers says that the average of the observed values gets close to the mean μ_x of x.

In this applet, we represent a random variable x as the total number of spots on the "up" faces of one or more dice.

Choose the number of dice by clicking FEWER DICE or MORE DICE. To see the roll totals or the population mean number of spots μ_x, check the corresponding box at the left. Fill in the number of rolls you'd like to make and click ROLL DICE. The graph shows the average x of the spots for all of your rolls. As you make more and more rolls, x should eventually get close to μ_x.