6.2 Suppose a random variable X has a probability density function given by f (x) = e kx (1 - x) 0 … x … 1 0 elsewhere a Find the value of k that makes this a probability density function.
b Find P (0.4 X 1).
c Find P (X 0.4 |X 0.8).
d Find F

(b) P (X

b) and sketch the graph of this function.