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In R, you can generate the data from multinomial distribution using rbinom. For example, if you do
rbinom(400, 1, 0.2)
It generates 400 points of 0 or 1 with the probability of 0.2 that the data point is 1. So, the second argument is the number of trials, but I don't exactly know that that means. What is the number of trials? If I set this to be 1, I see the values of 0 or 1, and if I set it to be N, I see the values of 0 - N.
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By ways of illustration, the probability of the success occurring less than 3 times if the number of trials is 10 and the probability of success is 0.3 is: As the binomial distribution is discrete, the previous probability could also be calculated adding each value of the probability function up to three:
The rbinom function can be used to simulate the outcome of a Bernoulli trial. This is a fancy statistical word for flipping coins . You can use it to calculate the number of successes in a set of pass/fail trials with success estimated at probability p .
Where P is the probability, n is the total number of trials and p is the probability of success. Where n is numbers of observations, N is the total number of trials, p is the probability of success.
If you want to obtain, for instance, 15 random observations from a binomial distribution if the number of trials is 30 and the probability of success on each trial is 0.1 you can type: Nonetheless, if you don’t specify a seed before executing the function you will obtain a different set of random observations.
The size is the total number of trials, of which size*prob are expected to be successes.
rbinom(400, size = 10, prob = 0.2)
gives the results of 400 runs of 10 coin flips each, returning the number of successes in each run.
So, rbinom(1, 10, 0.2) has the same expected value as sum(rbinom(10, 1, 0.2)).
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