Poisson Approximation to the Binomial

This applet illustrates the Poisson approximation for the binomial distribution.

The important points to remember and notice on the program in regard to the binomial are:

• Probabilities for the binomial are defined for integer values. As such, the binomial is said to be a probability mass function as the probabilities are concentrated (in mass) at distinct points.
• The cumulative probability function for the binomial is a step function. It has jumps at each integer where the probability mass changes.
• The binomial is characterized by the sample size n and the probability of success p. It has mean np and variance np(1-p).

The important points to remember and notice on the program in regard to the Poisson are:

• Probabilities for the Poisson are defined for integer values. As such, the Poisson is said to be a probability mass function as the probabilities are concentrated (in mass) at distinct points.
• The cumulative probability function for the Poisson is a step function. It has jumps at each integer where the probability mass changes.
• The Poisson is characterized by the mean u and the variance is equal to the mean. The approximating Poisson (to the binomial) has u=np.