X\Y 1 2
0 0.1 0.3
1 0.05 0.1
2 0.2 0.25sjaguar13 said:Given this joint PDF of X and Y:
Code:X\Y 1 2 0 0.1 0.3 1 0.05 0.1 2 0.2 0.25
So:
P(X = 1| X+Y=2) = 1/2?
P(X <= 1 and Y <= 2) = 1/3?
A joint PDF (probability density function) is a mathematical function that describes the probability of two or more random variables occurring simultaneously. It is used to calculate the likelihood of a specific outcome for multiple variables.
To find the probability of a joint PDF for X and Y, you need to integrate the function over the region of interest. This means that you must determine the bounds of the integral based on the given values for X and Y. Once the integral is solved, the resulting value is the probability of X and Y occurring together.
No, the probability of a joint PDF cannot be greater than 1. This is because the total probability of all possible outcomes must equal 1. If the probability of X and Y occurring together is greater than 1, it would violate this rule.
A joint PDF describes the probability of two or more variables occurring together, while a marginal PDF describes the probability of a single variable occurring. The marginal PDF is found by integrating the joint PDF over all possible values of the other variables.
Joint PDFs can be used to make predictions by calculating the probability of certain outcomes for multiple variables. This can be helpful in decision-making or risk analysis, as it allows you to estimate the likelihood of certain events occurring based on the given data.