TABLE OF CONTENTS The Binomial (Bernoulli) distribution is defined as
for k = 0, 1, 2, , n and 0 < p < 1. Therefore, b(k;n;p) is non-negative.
From (10.12) and (10.11),
and thus the binomial distribution b(k;n;p) is a pdf of the discrete type.
In (10.13), we call p the probability of a success. Likewise, we call q the probability of a failure.
Then,
For n = 2 and p = 1/2, (10.12) becomes
Moreover, for k = 0, 1 and 2, (10.15) reduces respectively to
The pdf and cdf of the binomial distribution for n = 2, p = 1/2, and k = 0, 1, and 2 are shown in Figures 10.1 and 10.2, We observe that they are the same as in Example 9.1, Chapter 9, Page 9 7,
A coin is tossed six times. Compute:
the probability that exactly (no more, no less) two heads show up
the probability of getting at least four heads
the probability of no heads.
the probability of at least one head.
Solution:
Here, n = 6. Let us denote p as a success if heads show up, and q as a failure if tails show up. Obviously, q = 1 ? p and p = q = 1/2.
We use the binomial distribution with k = 2...
