A joint pmf, or probability mass function, is a mathematical function that assigns probabilities to each possible combination of values for two or more random variables. In the context of "Find joint pmf of X and X+Y", the joint pmf represents the probabilities for the sum of two random variables, X and Y.
To find the joint pmf of X and X+Y, you will need to know the individual pmfs of X and Y, as well as the relationship between X and Y (in this case, X+Y). You can then use the joint pmf formula, which involves multiplying the individual pmfs for each combination of values.
Yes, the joint pmf of X and X+Y can be represented graphically in a two-dimensional plot, where the x-axis represents the values for X and the y-axis represents the values for X+Y. Each point on the plot represents a specific combination of values and the height of the point represents the probability of that combination occurring.
Calculating the joint pmf of X and X+Y can provide important insights into the relationship between these two random variables. It can also be used to calculate other useful statistics, such as the expected value and variance of X+Y. Additionally, it can be used to make predictions and decisions based on the probabilities of different combinations of values.
No, the joint pmf formula is only applicable for discrete random variables. For continuous random variables, the joint probability density function (pdf) is used instead. The concept is similar, but the formula and calculations are different.