Probability mass function

**Zennie** · October 20th 2010, 06:23 PM

The distribution of a random variable X is given by
$F(x) = \left\{ \begin{array}{lr} 0 & \text {if} \hspace {3pt} x <-2\\ \frac{1}{2} & \text {if} \hspace {3pt} -2 \leq x <2\\ \frac{3}{5} & \text {if} \hspace {3pt} 2 \leq x <4\\ \frac{8}{9} & \text {if} \hspace {3pt} 4 \leq x <6\\ 1 & \text {if} \hspace {3pt} x \geq 6\\ \end{array} \right$

Determine the probability mass function of X.

I have no idea where to begin. Can anyone show the process to determine the probability mass function so that I can repeat it for other problems?

**pickslides** · October 20th 2010, 07:06 PM

Isn't this already a pmf?

**Zennie** · October 20th 2010, 07:23 PM

Originally Posted by pickslides

Isn't this already a pmf?

Well, I didn't think so. But I'm not sure. I don't see why my textbook would have asked for the pmf if it was one already. My understanding was that this was the distribution function and the pmf could be gotten from this function. However, I could very well be wrong.

**Plato** · October 21st 2010, 03:07 AM

The given function is an cumulative distribution function, CDf.
You want its pdf.
$\begin{array}{*{20}c} \hline \vline & x &\vline & { - 2} &\vline & 2 &\vline & 4 &\vline & 6 & \\ \hline \vline & {f(x)} &\vline & {\frac{{45}} {{90}}} &\vline & {\frac{9} {{90}}} &\vline & {\frac{{26}} {{90}}} &\vline & {\frac{{10}} {{90}}} \\\end{array}$

Those are the 'jumps' at each value.

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