Expected Value Calculator

TATITIC CALCULATOR Expected Value A precise tool.
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What is the Expected Value & How does it work?

The expected value, often denoted (E[X]), represents the long‑run average outcome of a random variable if the experiment were repeated infinitely many times. It provides a single summary measure that captures the central tendency of a probability distribution.

For a discrete random variable with possible outcomes (x_1, x_2, dots, x_n) and corresponding probabilities (p_1, p_2, dots, p_n), the expected value is calculated by weighting each outcome by its probability and summing the results.

E[X] = sum_{i=1}^{n} x_i ; p_i
E[X] = expected value of X, x_i = i‑th possible outcome, p_i = probability of (x_i)

In the continuous case the sum becomes an integral: (E[X] = int_{-infty}^{infty} x f(x),dx), where (f(x)) is the probability density function. Understanding how to compute expected value is fundamental for decision‑making, risk assessment, and many statistical methods.

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Frequently Asked Questions
What is the formula for calculating expected value?
The expected value E[X] is calculated as the sum of each outcome multiplied by its probability: E[X] = x1*p1 + x2*p2 + ... + xn*pn.
How do I use this calculator if I have outcomes and probabilities?
Enter your outcomes in one field and their corresponding probabilities in another. The calculator will compute the expected value for you.
Can this calculator handle negative outcomes or probabilities?
Yes, the calculator can handle both negative outcomes and probabilities as long as they are valid within a probability distribution (0 <= p <= 1).
What if I have more than 10 outcomes to calculate?
This calculator is designed for up to 10 outcomes. For more, consider using statistical software or programming tools.
Is the expected value always a whole number?
No, the expected value can be a decimal or fraction depending on the outcomes and probabilities provided.
Can I use this calculator for continuous random variables?
This calculator is specifically for discrete random variables. For continuous variables, you would need to integrate over the probability density function.
What does the expected value tell me about my data?
The expected value provides a measure of the central tendency of your data, representing the long-run average outcome if the experiment were repeated many times.

Results are for informational purposes only and do not constitute professional advice.