Answer to Question #45894 in Statistics and Probability for Akshaya

Question

Let x be a continuous random variable with the probability distribution defined by
p(x)= {kx^2, 0<=x<=3
={0,else where

Evaluate k and find (i) P(1 ≤ x < 2), (ii) P(x ≤ 1),
(iii) P(x > 1). Also find the mean and variance of the distribution.