Find K So That the Function $f ( x ) = \left\{ \begin{array} { l l } k x ( 1 - x ) & \text { if } 0 < x < 1 \\0 & \text { otherwise }\end{array} \right.$

Multiple Choice

Find k so that the function $f ( x ) = \left\{ \begin{array} { l l } k x ( 1 - x ) & \text { if } 0 < x < 1 \\0 & \text { otherwise }\end{array} \right.$ can serve as the probability density function of a random variable X.

A) $\frac { 1 } { 3 }$
B) $\frac { 1 } { 6 }$
C) $\frac { 1 } { 2 }$
D) 1
E) 3
F) 6
G) 2
H) 0