Expected Value Calculator

Calculate the expected value (weighted average of outcomes) of a discrete probability distribution.

Expected Value E(X)

27.0000

प्रसरण241.0000
मानक विचलन15.5242
Sum of Probabilities1.0000

Expected Value E(X) vs Outcome 1

सूत्र देखें →

सूत्र

## How to Calculate Expected Value ### Formula **E(X) = Sum of (xi * pi)** The expected value is the long-run average outcome of a random variable. Multiply each possible outcome by its probability and sum the products. It represents the "center of gravity" of the probability distribution. The variance is E(X^2) - [E(X)]^2.

हल किया गया उदाहरण

A game pays $10 with probability 0.2, $20 with probability 0.5, and $50 with probability 0.3.

  1. 01E(X) = 10*0.2 + 20*0.5 + 50*0.3
  2. 02= 2 + 10 + 15 = 27
  3. 03E(X^2) = 100*0.2 + 400*0.5 + 2500*0.3 = 20 + 200 + 750 = 970
  4. 04Var(X) = 970 - 27^2 = 970 - 729 = 241
  5. 05SD = sqrt(241) ≈ 15.5242