Answer to Question #45598 in Statistics and Probability for Akshaya

Question

Let x be a continuous random variable with the probability distribution defined by


  

elsewhere
kx x
p x
0,
, 0 3
( )
2
. 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.