To simulate multiple draws from a random variable with a finite number of discrete outcomes, a multinomial sampling function is used. This function accepts the total number of draws and a vector of probabilities for each possible outcome. It returns a corresponding vector where each component represents the total count of occurrences for that specific outcome within the simulated sample.

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Sampling is the formal process of acquiring data by drawing independent realizations from an underlying random process. Collecting this empirical data is the necessary first step in using statistical methods to investigate and estimate unknown theoretical probabilities.

Sampling from a Random Process

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To simulate an event with a $$0.5$$ probability, such as a fair coin toss, we can utilize a random number generator that outputs continuous values in the interval $$[0, 1]$$. By testing whether the generated float is greater than $$0.5$$, we assign the two outcomes with equal likelihood, since the probability of the value falling in either the $$[0, 0.5]$$ or $$(0.5, 1]$$ sub-interval is exactly $$b-a = 0.5$$.

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