The cumulative distribution function, F(x), of a continuous random variable X is given by the following expression
F(x) =
0, x < 1
k(x^4 + 2x^2 - 3), 1 <= x <= 3
1, x > 3
where k is a positive constant.
a) The value of k is
b) Find P(X > 2)
c) The probability density function of X, for all values of x is
for 1 <= x <= 3