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It is cumulative when you add together the probabilities of all events resulting in the given number or fewer successes.

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It is cumulative when you add together the probabilities of all events resulting in the given number or fewer successes.

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The distribution depends on what the variable is.

If the key outcome is the number on the top of the die, the distribution in multinomial (6-valued), not binomial.

If the key outcome is the number of primes, composite or neither, the distribution is trinomial.

If the key outcome is the number of sixes, the distribution is binomial with unequal probabilities of success and failure.

If the key outcome is odd or even the distribution is binomial with equal probabilities for the two outcomes.

Thus, depending on the outcome of interest the distribution may or may not be binomial and, even when it is binomial, it can have different parameters and therefore different shapes.

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Sol Weintraub has written:

'Tables of the cumulative binomial probability distribution for small values of p' -- subject(s): Binomial distribution, Tables

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Two independent outcomes with constant probabilities.

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A discrete distribution is one in which the random variable can take only a limited number of values.

A cumulative distribution, which can be discrete of continuous, is the sum (if discrete) or integral (if continuous) of the probabilities of all events for which the random variable is less than or equal to the given value.

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