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Probability  Gravner69.b
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$f(x) = \begin{Bmatrix} cx & if (0<x<4) \\ 0 & otherwise \end{Bmatrix}$
(b) Compute $P(1\leqslant X\leqslant 2)$
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$P(1 \leq x \leq 2) = \Large \int_{1}^{2} c x = c \int_{1}^{2}x$
$\large = \frac{1}{8} \int_{1}^{2}x$
$\large = \frac{1}{8} \left [ \frac{x^2}{2} \right ]_1^{2}$
$= \Large\frac{3}{16}$
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Nov 27, 2019
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