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Given the following CDF

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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?

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  • $\begingroup$ This CDF is the CDF for the discrete distribution : $$P(1)=P(3)=P(5)=P(7)=\frac 14$$ $\endgroup$ – WW1 Sep 26 '19 at 15:52
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$P(T>3)=1-P(T \leq 3)=1-F(3)$. (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.)

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  • $\begingroup$ Can I write the second part as P(T >= 3)=1-F(3) + P(X = 3)? $\endgroup$ – user708015 Sep 26 '19 at 15:46
  • $\begingroup$ @user708015 Yes; $F(x)-\lim_{y \to x^-} F(x)=P(X=x)$. $\endgroup$ – Ian Sep 26 '19 at 16:08

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