Probability

Variance and Standard Deviation of X

Compute Var(X) = E(X²) − [E(X)]² and SD(X) from a discrete distribution. Enter x, P(x) pairs one per line.

Live Calculator · Step-by-Step · Probability
Inputs
Each line: x value, probability. Probabilities must sum to 1.
Result
Result
Enter values and calculate.
E(X)
—
= Σ x·P(x)
E(X²)
—
= Σ x²·P(x)
Var(X) = σ²
—
= E(X²)−[E(X)]²
SD(X) = σ
—
= √Var(X)

Step-by-Step Work

Your explanation will appear here.

PMF Chart — E(X) and ±1 SD region