Explain what is meant by this statement: "There is not just one normal probability distribution

Explain what is meant by this statement: "There is not just...

Key Concepts

Probability Distribution

A probability distribution describes how the values of a random variable are distributed, specifying the probability of each outcome or range of outcomes in a statistical experiment.

Normal Distribution

The normal distribution is a specific type of probability distribution that is symmetric and bell-shaped, where the bulk of the values lie around the mean, with its spread determined by the variance or standard deviation.

Family of Distributions

A family of distributions refers to a set of probability distributions that share a common functional form but differ based on the values of one or more parameters. In the case of the normal distribution, varying the mean and variance generates different individual distributions within the same family.

Parameterization

Parameterization is the process of defining a distribution in terms of its parameters. The normal distribution is parameterized by its mean and variance, meaning that each unique pair of values corresponds to a different distribution within the larger normal family.

Transcript

00:01 All right.

00:02 So we're talking about probability distributions and specifically the normal probability distribution.

00:09 And what does it mean where we say there's not just one normal probability distribution, but a family of normal probability distributions.

00:17 What does that mean? well, one of the nice things we can do is look at the bunch of graphs of these things.

00:23 So a lot of us have played with these graphing programs.

00:28 And this is this beastly looking for, formula, which is actually very amazing in the fact that it contains the number e, pi, root, two.

00:39 I mean, all these amazing mathematical constants.

00:42 But anyway, that's beside the point.

00:44 But this is the normal probability distribution formula.

00:49 And there's s is supposed to be sigma, just so you know, but i just have s here, which is the standard deviation.

00:57 And you can change the parameters of the standard deviation and the mean based on.

01:02 What the problem the the the scenario contains like maybe the mean of whatever it is is three and the standard deviation was say point three or whatever well not negative there we got kept that it then you make this maybe it's point uh point five i know whatever you want whatever the problem entails we've been doing work with all these calculations whatever you get i mean there's an infinite possibility of things that, of mews and of means and standard deviations that you can use here...

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