1)I actually have a doubt regarding this (given below): If X is an absolutely continuous random variable then it's distribution function f(x) is strictly increasing function and it can't attain the value zero at the points which are taken by the random variable i.e. it's CDF cannot be constant ?
2)I actually came by the doubt when i am seeing the prove of the probability integral transformation theorem for absolutely continuous random variable .As in the prove they consider the CDF of random variable to be strictly increasing instead of non-decreasing (WHY?)
If anyone failed to understand my 1st doubt please see 2) and help me to understand.