Getting the probability distribution of a random variable

[rcktbr]

Homework Statement

Described below

Relevant Equations

Marginal Probability Equation

X and Y are discrete random variables with the following joint distribution:

a) Calculate the probability distribution, mean, and variance of Y.

My attempt:

I have calculated the probability for different values of Y and X using the following equation: $\text{Pr(Y = y)}$ = $\sum_{i=1}^l$ $\rm{Pr(X = x_i, Y = y)}$. I have arrived at some results, such as $\text{Pr(Y = 14)} = 0.21$, $\text{Pr(Y = 22)} = 0.23$, $\text{Pr(Y = 30)} = 0.30$, $\text{Pr(Y = 40)} =0.15$ and $\text{Pr(Y = 65)} = 0.11$.

However, I wanted to know how the formula above could be used in calculating the probabilities. What would be $x_1$? What to put in i in an equation such as $\text{Pr(Y = 14)}$ = $\sum_{i=?}^?$ $\rm{Pr(X = x_i, Y = 14)}$?

 

[FactChecker]

With $i$ as a subscript of $x$ values, it should be $i=1,2,3$. You can then assign the values of the $x_i$s in whatever order you want. I would start from the top row to the bottom. $x_1=1,\ x_2=5,\ x_3=8$.

 

[rcktbr]

Alright. I will do the same for Y so. Thanks.