Ximpledu

Probability Distribution Table

See how to find the expected value, variance, and standard deviation
from a probability distribution table.
1 example and its solution.

Probability Distribution Table

Definition

Xx1x2x3...
P(X)p1p2p3...
X: Value for each case
P(X): Probability for each case

Formula

p1 + p2 + p3 + ... = 1 - [1]

E(X) = x1p1 + x2p2 + x3p3 + ... - [2]
V(X) = E(X2) - [E(X)]2 - [3] [4]
σ(X) = √V(X)
[1]
The sum of the probabilities is 1.
[3]
E(X2) = (x1)2p1 + (x2)2p2 + (x3)2p3 + ...
[4]
V(X): Variance
σ(X): Standard Deviation
Variance, Standard Deviation

Example

X-1123
P(X)14a1316


1. a = ?
2. Expected value = ?
3. Variance = ?
4. Standard deviation = ?
1. Solution
2. Solution
3. Solution
4. Solution