Question $4(25$ points$)$: Basics of Continuous of Distribution

Let the PDF of a continuous distribution be given as

$f_x(x)=K{x}^2,$ for $,-c_{1}x{c}_1$

$($a$)(5$ Pts$.)$ Determine $K$ and plot the PDF$.$ Comment on the result.

$($b$)(5$ Pts$.)$ Determine ${}_x.$ Comment on the result.

$($c$)$ Pts$.)$ Determine ${}_x^2.$ Comment on the result.

$($d$)(5$ Pts$.)$ Determine the CDF of $x,F_x(x),$ and plot it for $x-.$

$(e)(5Pts.)$ Determine the $MGFofx.$ Comment $on$ the result.

c$1=4$