If the probability density of a random variable is given by f(x)=kx(1−x), find the value of k and the probabilities:
(i) between 0.4 and 0.8
(ii) greater than 0.5.
a) k=6/5, (i) 0.06, (ii) 0.20
b) k=4/3, (i) 0.09, (ii) 0.33
c) k=2, (i) 0.20, (ii) 0.25
d) k=3/2, (i) 0.12, (ii) 0.50