Probability based on cumulative distribution function

by RAHUl JHa   Last Updated January 19, 2018 08:19 AM

I have the following cumulative distribution function:

$F(x)=\begin{cases} 0& \text{ if } x<0 \\ \frac{1}{4}+\frac{1}{6}(4x-x^2) & \text{ if } 0\leq x\leq1\\ 1& \text{ if } x\geq1 \end{cases} $

Now, it is required to calculate the probability $P(X=0|0\leqX\<1)$. How can I obtain the probability at a single point when the function given is a continuous function in the given range $0\leqX\<1$?

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