Mode of a continuous random variable

This article is a continuation from the previous article. It may be a good to read through it before attempting this article. This article explores the mode of a continuous random variable.

The mode is the value of the random variable where the p.d.f reaches its highest point. This is where it is most dense.

Below we shall look at some examples of finding the mode.

Example

The random variable X has probability density function f(x) where;
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We shall find the mode of f(x);
It is useful to sketch the graph when finding the mode. The sketch of the function is shown below;
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The mode occurs at the maximum point on the graph.
To find the maximum point we find where the gradient is equal to zero so we solve f(x)=0; that is;
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…so the mode is;
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