The probability density function of a random variable is defined by (x) = 4x - 3x 2

The probability density function of a random variable is defined by ƒ(x) = 4x - 3x² for x in [0, 1]. Find the following for the distribution.
(a) The mean
(b) The standard deviation
(c) The probability that the value of the random variable will be less than the mean
(d) The probability that the value of the random variable will be within 1 standard deviation of the mean