Probability - Gravner-69.a

Question

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

(a) Determine $c$.

Answer 1

$\Large \int_{0}^{4} cx \ dx = 1$

 

$\Large c$ $\Large \int_{0}^{4} x \ dx = 1$

 

$\Large c$ $\Large \left [ \frac{x^2}{2} \right ]_{0}^{4} = 1$

 

$8c =1 $

$\large c = \frac{1}{8}$

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Part b