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.
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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A distribution that is NOT normal. Most of the time, it refers to skewed distributions.
Because very many variables tend to have the Gaussian distribution. Furthermore, even if the underlying distribution is non-Gaussian, the distribution of the means of repeated samples will be Gaussian. As a result, the Gaussian distributions are also referred to as Normal.
Not necessarily.
The height of adult males in your nearest town.
No, the normal distribution is strictly unimodal.
A distribution that is NOT normal. Most of the time, it refers to skewed distributions.
Certainly.
example from your business or industry that seems to reflect the normal distribution
Because very many variables tend to have the Gaussian distribution. Furthermore, even if the underlying distribution is non-Gaussian, the distribution of the means of repeated samples will be Gaussian. As a result, the Gaussian distributions are also referred to as Normal.
True * * * * * No. The Student's t-distribution, for example, is also bell shaped.
Not necessarily.
The standard normal distribution is a normal distribution with mean 0 and variance 1.
The standard normal distribution is a special case of the normal distribution. The standard normal has mean 0 and variance 1.
le standard normal distribution is a normal distribution who has mean 0 and variance 1
The height of adult males in your nearest town.
When its probability distribution the standard normal distribution.
No, the normal distribution is strictly unimodal.