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When the event of interest is a cumulative event.

For example, to find the probability of getting three Heads in 8 tosses of a fair coin you would use the regular binomial distribution. But to find the probability of up to 3 Heads you would use the cumulative distribution.

This is because

Prob("up to 3") = Prob(0 or 1 or 2 or 3) = Prob(0) + Prob(1) + Prob(2) + Prob(3) since these are mutually exclusive.

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Q: When to use cumulative binomial probability?

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This is a binomial probability distribution. The number of trials, n, equals 30; and the probability of success is p, which is 0.1. In this problem, you want the probability of at least 5, which is the complement of at most 4. We use the complement because we can subtract from 1 that probability and we will have the solution. The related link has the binomial probability distribution table which is cumulative. Per the table, at n=30, p=0.1 and x = 4; the probability is 0.825. Therefore the probability of at least 5 is 1 - 0.825 or 0.175.

The mean of a binomial probability distribution can be determined by multiplying the sample size times the probability of success.

The symbol for probability of success in a binomial trial is the letter p. It is the symbol used for probability in all statistical testing.

proportional to the cumulative probability of all the causes listed for that hazard

This depends on what information you have. If you know the success probability and the total number of observations, you can use the given formulas. Most of the time, this is the case. If you have data or experience which allow you to estimate the parameters, it may sometimes happen that you work like this. This mostly happens when n is very large and p very small which results in an approximation with the Poisson distribution.

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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

What is the symbol for a Probability of success in a binomial trial?

This is a binomial probability distribution. The number of trials, n, equals 30; and the probability of success is p, which is 0.1. In this problem, you want the probability of at least 5, which is the complement of at most 4. We use the complement because we can subtract from 1 that probability and we will have the solution. The related link has the binomial probability distribution table which is cumulative. Per the table, at n=30, p=0.1 and x = 4; the probability is 0.825. Therefore the probability of at least 5 is 1 - 0.825 or 0.175.

The mean of a binomial probability distribution can be determined by multiplying the sample size times the probability of success.

The symbol for probability of success in a binomial trial is the letter p. It is the symbol used for probability in all statistical testing.

The binomial probability distribution is discrete.

proportional to the cumulative probability of all the causes listed for that hazard

The skew binomial distribution arises when the probability of a particular event is not a half.

Normal distribution is the continuous probability distribution defined by the probability density function. While the binomial distribution is discrete.

We can use it to find the coefficients of numbers when we expand a binomial. We also use it in probability theory. In fact there are many uses for it.

p

This depends on what information you have. If you know the success probability and the total number of observations, you can use the given formulas. Most of the time, this is the case. If you have data or experience which allow you to estimate the parameters, it may sometimes happen that you work like this. This mostly happens when n is very large and p very small which results in an approximation with the Poisson distribution.

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