/* Example code for finding Poisson probabilities in SAS */

OPTIONS pagesize=50 linesize=64; 
/* (setting the page margins) */

/* The command POISSON computes _cumulative_ poisson probabilities */

/* To get the cumulative probability, the syntax is: poisson(lambda, x) */
/* where lambda and x are values that you fill in */

/* Suppose our random variable X is Poission with lambda = 12.33. */

/* Let's answer the following questions */
/* 1. What is the probability of 15 or fewer occurrences?  P(X <= 15) */
/* 2. What is the probability of EXACTLY 6 successes? P(X = 6) */
/* 3. What is the probability of more than 13 successes? P(X > 13) */
/* 4. What is the probability of 13 or more successes? P(X >= 13) */
/* 5. What is the probability of 8, 9, or 10 successes? P(8 <= X <= 10) */

/* This SAS program will give us the answers to all these questions in an instant */
/* I will label the answers to the 5 questions as prob1, prob2, ... , prob5. */

data poiss;

prob1 = poisson(12.33, 15);

prob2 = poisson(12.33, 6) - poisson(12.33, 5);

prob3 = 1 - poisson(12.33, 13);

prob4 = 1 - poisson(12.33, 12);

prob5 = poisson(12.33, 10) - poisson(12.33, 7);

run;

proc print data=poiss;
title 'Poisson Probabilities';
run;

/* After we input this program into the program editor and run the code */
/* Then the results print in the Output window */

/* The difference is:  SAS can do these for any lambda, whereas the table only */
/* gives probabilities for certain lambda choices. */