1.4. Consider an experiment in which a certain event will occur with probability ah and will not occur with probability 1 - ah, where a is a fixed positive parameter and h is a small (h

(a) The probability that the event never occurs during the n trials is 1 - nah + o(h);

(b) The probability that the event occurs exactly once is nah + o(h);

(c) The probability that the event occurs twice or more is o(h).

Hint: Use the binomial expansion

Transcribed Image Text:

- = (1 ah)" 1 nah + - n(n - 1) 2 -(ah)- -