Probability with Chi-Square distribution What is the difference, when calculating probabilities of Chi-Square distributions, between $<$ and $\leq$ or $>$ and $\geq$. 
For example, say you are asked to find P$(\chi_{5}^{2} \leq 1.145)$. 
I know that this is $=0.05$ from the table of Chi-Square distributions, but what if you were asked to find P$(\chi_{5}^{2} < 1.145)$? How would this be different?

The $\chi^2$ distributions  are continuous distributions. If $X$ has continuous distribution, then
$$\Pr(X\lt a)=\Pr(X\le a).$$
If $a$ is any point, then $\Pr(X=a)=0$. So in your case, the probabilities would be exactly the same. 
Many other useful distributions, such as the normal, and the exponential, are continuous. 
