Let the probability density function PDF of a random variable X takes the form c(3x^2+2x) for 0<=x<=2 and 0 otherwise.
a) Find the constant c such that the PDF is legitimate.
b) What is the probability that X > 1?
c) Find the Standard Deviation of X.
d) P(X>1|X<1.5) e) Find the first and third quartiles.