# PMF and CDF Probability doubt

Given the following CDF

what is

$$P(T > 3)$$

If it was T greater than or equal to 3, how would the answer change? Will we add the probability of 3 in the answer?

• This CDF is the CDF for the discrete distribution : $$P(1)=P(3)=P(5)=P(7)=\frac 14$$ – WW1 Sep 26 '19 at 15:52

$$P(T>3)=1-P(T \leq 3)=1-F(3)$$. (In this case $$P(T=3)$$ is included in the subtraction and thus is not included in the final result, as it should be.)
$$P(T \geq 3)=1-P(T<3)=1-\lim_{t \to 3^-} F(t)$$. (In this case $$P(T=3)$$ is not included in the subtraction and thus is included in the final result, again as it should be.)
• @user708015 Yes; $F(x)-\lim_{y \to x^-} F(x)=P(X=x)$. – Ian Sep 26 '19 at 16:08