What is an example of non normal distribution?

Answer 1

Hey there! Great question! Non-normal distributions are super common in the real world. Let me give you an example from my own life.

Imagine you're at a family reunion, and you decide to measure the heights of all your relatives. You'd probably expect the heights to follow a nice, normal distribution curve, right? Well, in my family, that's not the case. We have this one uncle, let's call him Bob, who's a towering 6 feet 9 inches, and then there's his twin brother, Joe, who's a mere 5 feet 5 inches. Now, if you plot all the heights on a graph, you won't get that classic bell curve; instead, you'll see two distinct peaks – one for the super tall folks and another for the shorter ones. This is a classic example of a bimodal distribution, a type of non-normal distribution where you have two or more peaks instead of the usual single hump.

Non-normal distributions like this can be found in various fields, from finance to Biology. They remind us that the world isn't always neatly packed into that familiar bell-shaped curve, and understanding these deviations is essential for making accurate predictions and decisions in many areas of life. So, don't be surprised if you come across more of these quirky distributions – they're a testament to the rich diversity of data in our world!

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Answer 2

The uniform distribution.

A random variable X is said to have a [standard] uniform distribution over the interval [0, 1] if

Pr[a < X < b = (b- a) for 0 ≤ a ≤ b ≤ 1

and

Pr[X] = 0 elsewhere.

The probability of the variable being within a range is equal to the size of that range.

The discrete version of this is the probability distribution of the number shown in the throw of a die.

Pr[Number = n] = 1/6 for n = 1, 2, 3, 4, 5 or 6

and 0 otherwise.