Binomial Distribution: What Is It?

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The binomial distribution describes the probability of a specific number of successes in a series of independent events, each with a probability p of success. It is represented mathematically as Bin(n,p), where x can range from 0 to n. The independence of events allows for the use of the product identity in calculating probabilities. While the binomial distribution can lead to a normal distribution under certain conditions, it is not classified as a product distribution in the traditional sense. Understanding these distinctions is crucial for applying the binomial distribution correctly in statistical analysis.
aaaa202
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Is the binomial distribution, what you call a product distribution? How can I see that, if that is true?
 
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Hey aaaa202 and welcome to the forums.

The binomial distribution represents n independent events happening with each true event having a p probability of occurring.

In other words Bin(n,p) gives the probability distribution for having x events become true for x = 0 to x = n.

Because of the independence of each event, you can use the product identity P(A and B) = P(A)P(B) to generate the mathematical formula for getting a specific probability.
 
so it's a product distribution right? I've seen several physical examples of product distributed properties, and they all follow a normal distribution. Is this a general thing?
 

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