Find marginal CDF from joint PMF

discrete mathematicsprobability distributions

If I have the joint PMF:
$$P_{X,Y}(x,y)=\begin{cases} 0.01, & x,y=1,2,3,\ldots,10 \\ 0, & \text{otherwise}
\end{cases}$$
How would I proceed if I want to find $F_X(x)$ from here? I now this equation:
$$F_X(x) = \lim_{y \to \infty} F_{X,Y}(x,y)$$
But how do I find the joint CDF from the joint PMF?

Best Answer

Observe that your joint pmf is the product of 2 independent uniform (discrete uniform) distributions thus

$$P(X=x)=\frac{1}{10}$$

for $X \in \{1,2,3,\dots,10\}$

... in this case it is easier to find the marginal pmf first and then sum it to get its CDF

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