Surely this isn't right? did you mean x^2/2, so that F is continuous at x=1?I have been asked to determine the pdf given a DF.
F(x) = 0 for x<0
F(x) = x^2/x for x 0<= x < 1
You don't need the pdf at all to answer that question. F(x) is the probability that the random variable is between 0 and x. The probablity that x is between 0 and 1 is just F(1)= 1/2.F(X) = x/2 for 1<=x<2
F(x) = 1 for x>= 2
Is the pdf the derivative of the df
So if you wanted the probability of x between 0 and 1
The pdf would just be x ?