Let N be a
binomial random variable with parameters M and p, written B(M, p).
The mean and variance for the
binomial random variable are E (X) = np and var (X) = np(1 - p), respectively.
Neutrosophic
Binomial Random Variable: It is defined as the number of success when we perform the experiment n [greater than or equal to] 1 times, and is denoted as 'x'.
For any [mu] [member of] [R.sup.+] and [theta] [member of] [R.sup.+], a Negative
Binomial random variable X ~ NB([mu], [theta]) has the probability mass function
In general, we have the following inequality for the tail of
binomial random variable:
It would then not be appropriate to test the fit of the model by using a hypothesis test that assumes the number of dry days in 1999-2008 is a
binomial random variable with distribution Bi(3653, [p.sub.10]), since that number is not a random variable at all.
In this model, the calling frequency corresponding to sample i (a particular day and hour) is a
binomial random variable with sample size 12, and probability [P.sub.i] .
In view of the Bernoulli model, [L.sub.n] is distributed like a
binomial random variable on n independent trials with rate of success q in each.
Let X be a
binomial random variable with parameters n and p, where p denotes the defect level of process, and let [??] = X/n be the sample defect level.
The
binomial random variable r represents the number of successes in n trials of the experiment, and we know from an earlier chapter that the mean and variance of the binomial are
For this model, the number of links in the predation matrix is a
binomial random variable with n(n - 1)/2 trials and success probability y/n, so that the expected number of links is [Gamma](n - 1)/2 (i.e., approximately linear in n).
Since [r.sub.i] is a
binomial random variable with parameters [n.sub.i] and [[pi].sub.i], the variance of [p.sub.i] is [[pi].sub.i](1 - [[pi].sub.i])/[n.sub.i].
