Determine the probability mass function of (X) from the following cumulative distribution function: [ F(x)=left{begin{array}{lr} 0 &

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Determine the probability mass function of \(X\) from the following cumulative distribution function:

\[ F(x)=\left\{\begin{array}{lr} 0 & x. \]

Figure 3.3 displays a plot of \(F(x)\). From the plot, the only points that receive nonzero probability are \(-2,0\), and 2 . The probability mass function at each point is the jump in the cumulative distribution function at the point. Therefore,

\[ \begin{aligned} & f(-2)=0.2-0=0.2 \\ & f(0)=0.7-0.2=0.5 \\ & f(2)=1.0-0.7=0.3 \end{aligned} \]

Figure 3.3

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Applied Statistics And Probability For Engineers

ISBN: 192504

7th Edition

Authors: Montgomery, Douglas C., Runger, George C.

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