Probability - Gravner-69.b

Question

$f(x) = \begin{Bmatrix} cx & if (0<x<4) \\ 0 & otherwise \end{Bmatrix}$

(b) Compute $P(1\leqslant X\leqslant 2)$

Answer 1

$P(1 \leq x \leq 2) = \Large \int_{1}^{2} c x = c \int_{1}^{2}x$

$\large = \frac{1}{8} \int_{1}^{2}x$

$\large = \frac{1}{8} \left [ \frac{x^2}{2} \right ]_1^{2}$

$= \Large\frac{3}{16}$

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Part c