I would like to compute the variance of a continuous random variables distribution that has the following form:
When "a" becomes as small as zero, the parallelogram will become a rectangle, in this case, the variance should be zero, then high variance when "a" is large, and then variance go back to zero when "a" is very very large
However, when I integrate the CDF function I don't get zero variance at all. Below is my CDF (f(x)):
x --> 0 < x < a (red segment)
1/(b-a) --> a < x < a+b (blue segment)
x-b --> b < x < a+b (green segment)
I used the following variance equation, but I didn't get zeros variance when X was zero
What did I do wrong here? I appreciate your advice and suggestions