Suppose that X and Y have the following joint probability...

Suppose that $X$ and $Y$ have the following joint probability distribution: \begin{tabular}{cc|cc} & \multicolumn{2}{|c} {$x$} \\ \cline { 2 - 4 }$f(x, y)$ & 2 & 4 \\ \hline & 1 & 0.10 & 0.15 \\ $y$ & 3 & 0.20 & 0.30 \\ & 5 & 0.10 & 0.15 \end{tabular} (a) Find the marginal distribution of $X$. (b) Find the marginal distribution of $Y$.

Suppose that $X$ and $Y$ have the following joint probability distribution:
\begin{tabular}{cc|cc}
& \multicolumn{2}{|c} {$x$} \\
\cline { 2 - 4 }$f(x, y)$ & 2 & 4 \\
\hline & 1 & 0.10 & 0.15 \\
$y$ & 3 & 0.20 & 0.30 \\
& 5 & 0.10 & 0.15
\end{tabular}
(a) Find the marginal distribution of $X$.
(b) Find the marginal distribution of $Y$.

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Joint Probability Distribution

A joint probability distribution characterizes the probability of different combinations of outcomes for two or more random variables. It provides a complete description of the relationship between these variables by giving the probability for each possible pair (or tuple) of outcomes. This concept is essential because it lays the foundation for deriving other associated distributions, such as marginal and conditional distributions.

Marginal Distribution

A marginal distribution is the probability distribution of a subset of random variables obtained by summing or integrating out the unwanted variables from the joint probability distribution. In the context of two random variables, the marginal distribution for one variable is found by summing the joint probabilities over all values of the other variable. This process isolates the behavior of a single variable and is fundamental in probability and statistics when analyzing the properties of one variable independent of others.

Transcript

Please give Ace some feedback