Thread: Probability Density Functions
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Old October 27th, 2009, 04:45 AM
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F(x)=\int_{0}^{x}xdx, \;\ 0 \;\ to \;\ 1

F(x)=\int_{0}^{1}xdx=\frac{1}{2}

F(x)=\int_{1}^{2}(2-x)dx

\frac{1}{2}+\int_{1}^{x}(2-x)dx=2x-\frac{x^{2}}{2}-1

F(x)=\begin{Bmatrix}0, \;\ x\leq 0\\ \frac{x^{2}}{2}, \;\ 0<x<1\\ 2x-\frac{x^{2}}{2}-1, \;\ 1\leq x<2\\ 1, \;\ 2\leq x\end{Bmatrix}

P(.8 < x < 1.2)=\int_{.8}^{1}xdx+\int_{1}^{1.2}(2-x)dx
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