# Probability mass function

• Oct 20th 2010, 06:23 PM
Zennie
Probability mass function
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?
• Oct 20th 2010, 07:06 PM
pickslides
• Oct 20th 2010, 07:23 PM
Zennie
Quote:

Originally Posted by pickslides

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.
• Oct 21st 2010, 03:07 AM
Plato
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.