Suppose the reaction time (in seconds) to certain stimulus is a continuous random variable X with cumulative distribution function of the form
F(x) => 0 x < 1
=> ((x^2) ? 1 )/8 1 ? x ? 3
=> 1 x > 3
Determine the following:
(a) Derive the pdf of X.
(b) Derive the probability of reaction time of being less than 2.5 seconds.
(c) Derive the expected value of X.
(d) Derive variance of X