Explain the meaning of a distribution function with an example. How do you get the density function from the distribution function? Suppose that a continuous random variable X has a cumulative distribution function given by:
Fx =
2x^2 + 15x, for x > 0
-3x^2 + 23x - x/5, for 1 ≤ x ≤ 2
5x + 1, for x > 2
Find the probability density function of x. And hence compute the probability:
a) P(0.5 ≤ x ≤ 1)
b) P(1.25 ≤ x ≤ 1.75)
c) P(x ≤ 0.5)
d) P(x ≤ 1.5)