Contents
- ๐ What is this?
- ๐จ๐ปโ๐ป How to use it?
- ๐ฐ Examples
- ๐ Nuances
- ๐ค Frequently asked questions
- ๐ Related materials
What expected value tells you
Expected value is the probability-weighted average of every possible numeric outcome. It describes the long-run result of repeated trials, not a promise about the next trial.
How to enter a complete distribution
Put one outcome and its probability in each row. Probabilities are percentages from 0 to 100 and must total 100%. Negative outcomes can represent losses.
The calculator multiplies each outcome by its probability and adds the products. Variance and standard deviation show how widely outcomes sit around the average.
Three checks with familiar numbers
For -100 at 40%, 0 at 30% and 200 at 30%, E(X) is 20, variance is 15,600 and standard deviation is about 124.9.
A fair die has expected value 3.5 although no face shows 3.5. For 0 at 99% and 100 at 1%, E(X) is 1 and standard deviation is about 9.95.
Rows must be mutually exclusive and cover all possibilities. Keep one unit throughout, include costs in net outcomes, and compare standard deviation as well as the mean.
Reading the answer without hiding risk
Rows must be mutually exclusive and cover all possibilities. Keep one unit throughout, include costs in net outcomes, and compare standard deviation as well as the mean.
Questions about expected value
These answers cover percentages, negative outcomes and interpretation.
Why must probabilities total 100%?
The rows must describe every possible outcome of one trial.
Can an outcome be negative?
Yes. Negative values can represent losses, costs or penalties.
How do I enter 12.5%?
Enter 12.5 without the percent sign.
Can E(X) be absent from the outcomes?
Yes. A weighted average can lie between possible results.
Does a positive expected value guarantee a gain?
No. A finite run can differ substantially from the long-run average.
Similar calculators
You may find the following calculators on the same topic useful:
- Time duration calculator. Enter a start and end time to find the net duration, then add more intervals when the time is split.
- Fraction addition calculator. Enter two fractions, choose an operation and get an exact reduced answer.
- Divisors of a number calculator. Enter a positive whole number to see how many divisors it has, then open the complete list.
- Mean absolute deviation calculator. Enter numbers to see how far they lie from their arithmetic mean on average.
- Median absolute deviation calculator. Enter numbers to find the typical distance from their median.
- Fraction to decimal calculator. Enter a numerator and denominator to see the decimal value; add a whole part if needed.
- Coefficient of variation calculator. Enter a list of numbers to see their relative spread as a percentage.
- Variance calculator. Paste numbers, choose a data type, and see how far the values spread around their mean.
- Percentile and percentile rank calculator. Enter numbers, then choose a percentile or compare one value with the list.
- Bayes theorem calculator. Use the event rate, signal sensitivity and false-alarm rate to update the probability after a signal.
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