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[Run hard@thehsc]

What are the main differences between binomial, normal and Bernoulli distribution? I know what these mean individually, but find it hard to differentiate and compare these three types of differentiation...

 

[jimmysmith560]

Normal distribution describes continuous data which have a symmetric distribution, with a characteristic "bell" shape. The normal distribution is the most important continuous distribution. It is a good model for many characteristics that occur in nature, commerce, etc. For example, heights and weights, IQ, sales figures, package fill weights and so on. Such elements are all well modelled by a normal distribution. It is also known as the Gaussian distribution, named after the famous mathematician Carl Friedrich Gauss.

All normal distributions look like a symmetric, bell‐shaped curve, as shown below:



On the other hand, binomial distribution describes the distribution of binary data from a finite sample. It therefore gives the probability of getting events out of trials. In the binomial distribution, all eligible phenomena are studied.

While I did not study the Bernoulli distribution, it appears that this distribution represents the success or failure of a single Bernoulli trial. The difference between the Bernoulli distribution and the binomial distribution is that the latter represents the number of successes and failures in independent Bernoulli trials for some given value of .

I hope this helps!

 

[cossine]

What are the main differences between binomial, normal and Bernoulli distribution? I know what these mean individually, but find it hard to differentiate and compare these three types of differentiation...

binomial/bernoulli and normal distribution are completely different.

normal distribution is probability density function (pdf). pdf is just fancy way of saying functions that models the probability of continuous random variable.

binomial/bernoulli are probability mass function (pmf). pmf is just fancy way of saying function models that models the probability of discrete random variable.

Def discrete: opposite continuous

The binomial distribution has an "n" (number of trials) parameter. The bernoulli has only 1 trial hence does not have an n parameter. I would suggest you read the textbook to get a better answer.

 

[cossine]

Normal distribution describes continuous data which have a symmetric distribution, with a characteristic "bell" shape. The normal distribution is the most important continuous distribution. It is a good model for many characteristics that occur in nature, commerce, etc. For example, heights and weights, IQ, sales figures, package fill weights and so on. Such elements are all well modelled by a normal distribution. It is also known as the Gaussian distribution, named after the famous mathematician Carl Friedrich Gauss.

All normal distributions look like a symmetric, bell‐shaped curve, as shown below:

View attachment 35642

On the other hand, binomial distribution describes the distribution of binary data from a finite sample. It therefore gives the probability of getting events out of trials. In the binomial distribution, all eligible phenomena are studied.

While I did not study the Bernoulli distribution, it appears that this distribution represents the success or failure of a single Bernoulli trial. The difference between the Bernoulli distribution and the binomial distribution is that the latter represents the number of successes and failures in independent Bernoulli trials for some given value of .

I hope this helps!

The Bernoulli would have n = 1.

 

[Run hard@thehsc]

The Bernoulli would have n = 1.

true whereas we would use binomial for multiple n and normal when the n gets quite large, considering the distribution fits a given criteria

 

[dan964]

What are the main differences between binomial, normal and Bernoulli distribution? I know what these mean individually, but find it hard to differentiate and compare these three types of differentiation...

Bernoulli is a specific case of binomial distribution. Bernoulli would be saying flipping an individual coin and the probability it is a particular outcome say heads. Binomial would be flipping multiple coins and choosing one of them and the probability of it being a heads. Basically true/false. It is a discrete function as well, each probably/event is a discrete value.

Normal distribution are more like bell curves and are continuous probability functions. Often such functions may originate with discrete functions and then doing a generalisation e.g. the % of rolling a dice to get a 1. Generally uses continuous data e.g. average temperature for a month