Median of a continuous random variable

This article is a continuation from the previous article. It may be a good idea to go through it before attempting this article;
If X is a continuous random variable with cumulative density function c.d.f F(x) then the median, m, of X is given by; [IMAGE]
Let us look at some examples below;

Example

In this example a continuous random variable X has probability density function;
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First let us find the cumulative distribution function of X. We have done this in the previous; To find the cumulative function given the probability density function we integrate and we saw two ways of doing this; We could integrate between x and 0 or;
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…we know that F(0)=0, therefore C=0;
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Now we shall find the median of the function above. We saw that; If X is a continuous random variable with c.d.f F(x) then the median of X is F(m)=0.5, so we have;
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Now we must find the value of m;
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Here we select the value that is in the range of F(x) i.e 0≤x≤1.