4. Let ( X ) be a continuous random variable with a density function,
[
f(x)=left{egin{array}{ll}
a x^{2} & 0<x<2, \
0 & ext { otherwise }
end{array}
ight.
]
(a) (5 points) Find a.
(b) (5 points) Find the variance of ( X ).
(c) (5 points) Find the cumulative distribution function (cdf) of ( X ).
