# binomial random variable

## binomial random variable

[bī¦nō·mē·əl ‚ran·dəm ′ver·ē·ə·bəl]
(statistics)
A random variable, parametrized by a positive integer n and a number p in the closed interval between 0 and 1, whose range is the set {0, 1, …, n} and whose value is the number of successes in n independent binomial trials when p is the probability of success in a single trial.
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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].

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