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Suppose that $X$ has the Binomial distribution with parameters $n,p$ . How can I show that if $(n+1)p$ is integer then $X$ has two mode that is $(n+1)p$ or $(n+1)p-1?$
Usually the mode of a binomial B(n, p) distribution is equal to ⌊ (+) ⌋, where ⌊ ⌋ is the floor function. However, when ( n + 1) p is an integer and p is neither 0 nor 1, then the distribution has two modes: ( n + 1) p and ( n + 1) p − 1 .
The mode of the binomial distribution if (n + 1) is non integer; mode (μ 0) = the largest integer contained in (n + 1)p. if (n + 1) is integer; mode (μ 0) = (n+1) p and (n+1)p - 1
The binomial distribution is, in essence, the probability distribution of the number of heads resulting from flipping a weighted coin multiple times. It is useful for analyzing the results of repeated independent trials, especially the probability of meeting a particular threshold given a specific error rate, and thus has applications to risk ...
The Binomial Distribution. "Bi" means "two" (like a bicycle has two wheels) ... ... so this is about things with two results. Tossing a Coin: Did we get Heads (H) or. Tails (T) We say the probability of the coin landing H is ½. And the probability of the coin landing T is ½. Throwing a Die: Did we get a four ... ? ... or not?
The distribution of the number of experiments in which the outcome turns out to be a success is called binomial distribution. The distribution has two parameters: the number of repetitions of the experiment and the probability of success of an individual experiment.
10 Αυγ 2020 · Definition: Binomial distribution. Suppose the probability of a single trial being a success is p. Then the probability of observing exactly k successes in n independent trials is given by \[ \binom {n}{k} p^k (1 - p)^{n - k} = \dfrac {n!}{k!(n - k)!} p^k (1 - p)^{n - k} \label {3.40}\]
