For the random variable X with the given density function below:
f(x) = k(x 2 + a), if ? a ? x ? 0
k(a ? x 2 ), if 0 < x ? a
0, otherwise ? ? ?
(a) Find k in terms of a.
(b) Take a = last digit of your student id number (if it is 0, take it to be 9), then draw the graph of probability density function f(x).
(c) Determine the cumulative distribution function F(x).
(d) Compute E[X]. (This is called first moment of X.)
(e) Compute E[X2 ]. (This is called second moment of X.)
(f) Determine P(X ? 1 a ).