Lecture 13 Bernoulli’s Formula. The Most Probable Number of Occurrences of an Event If n

Lecture 13

Bernoulli’s Formula. The Most Probable Number of Occurrences of an Event

If n independent trials are performed in each of which the probability of occurrence of the event A is the same and is equal to p, then the probability of the event A occurring m times in these n trials is expressed by Bernoulli’s formula:



where . Thus we have











Definition. The number is called the most probable number of occurrences of the event A in n trials if at the value of is not less than all the other values of , i.e.

at .

If and , the number can be determined from the double inequality

.