Joint Probability Distributions - Theory & Concepts

Joint probability mass/density functions, marginal and conditional distributions, covariance, and correlation.

Engineering Data Analysis

Discrete Joint Probability Explorer

Probability Distribution Table

$X \setminus Y$	$Y = 1$	$Y = 2$	$Y = 3$	$g(x)$
$X = 10$				0.150
$X = 20$				0.600
$X = 30$				0.250
$h(y)$	0.200	0.500	0.300	1.000

Mean

\mu_X

21.00

Mean

\mu_Y

2.10

Covariance

\text{Cov}(X,Y)

2.9000

If $\text{Cov}(X,Y) > 0$ , X and Y tend to increase together. If $\text{Cov}(X,Y) < 0$ , they vary inversely. If $0$ , there is no linear relationship.

Probability Distribution Visualizer

Y=1

Y=2

Y=3

g(x)

X=10

0.10

0.05

X=20

0.10

0.40

0.10

X=30

0.05

0.20

h(y)

Bubble size & opacity indicate the magnitude of the joint probability $f(x,y)$ .

Green bars represent the marginal distributions $g(x)$ and $h(y)$ .

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Engineering Data Analysis

Probability Distribution Table

Probability Distribution Visualizer

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