A continuous probability density function is defined on the closed interval $[ 0 , a ]$ for a random variable $X$. When the random variable $X$ satisfies the following conditions, what is the value of the constant $k$? [4 points]\\
(가) For all $x$ where $0 \leq x \leq a$, $\mathrm { P } ( 0 \leq X \leq x ) = k x ^ { 2 }$.\\
(나) $\mathrm { E } ( X ) = 1$\\
(1) $\frac { 9 } { 16 }$\\
(2) $\frac { 4 } { 9 }$\\
(3) $\frac { 1 } { 4 }$\\
(4) $\frac { 1 } { 9 }$\\
(5) $\frac { 1 } { 16 }$