Expected Value Calculator
Calculate the expected value of a discrete random variable with ease. Visualize probabilities and outcomes instantly.
Input Values
Enter comma-separated values for outcomes and their corresponding probabilities.
Results
Probability Distribution Visualization
Understanding Expected Value
Expected Value (E[X]) is a fundamental concept in probability theory that represents the average value you would expect to obtain if you repeated an experiment or random process a large number of times. For a discrete random variable X, it's calculated by multiplying each possible outcome (xᵢ) by its probability (pᵢ) and summing these products.
Formula: The formula for expected value is given by: $$ E[X] = \sum_{i=1}^{n} x_i p_i = x_1p_1 + x_2p_2 + ... + x_np_n $$
Example: Consider a simple game where you win $10 if a fair coin lands heads and lose $5 if it lands tails. The outcomes are $10 and -$5, each with a probability of 0.5. The expected value is E[X] = (10 * 0.5) + (-5 * 0.5) = 5 - 2.5 = $2.5. This means on average, you can expect to win $2.50 per game if you play many times.
This tool is useful in various fields like finance, gaming, and decision making to assess the average outcome of probabilistic events.
Learn more about Expected Value on resources like Wikipedia.