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Probability distribution calculator

Calculate mean and variance for a discrete distribution with values and probabilities you supply.

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Probability distribution calculator processes your input in this browser. Inputs and results are excluded from analytics. Recent tools save tool names, visit counts and last-visit times. Saved tools store only their names. Draft saving is optional and stays on this device; delete saved text with the draft controls. Loading text from a URL is optional and contacts that server; its URL and your IP address are visible to the server. An optional “Use in” action keeps a handoff in this tab. The next tool removes it on arrival and ignores it if more than a minute has passed.

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Answer

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Calculate mean and variance for a discrete distribution with values and probabilities you supply.

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Precision and calculation record
Rounding changes displayed numbers, not the calculation. Text, fractions, matrices and CSV schedules keep their own formatting. Automatic keeps up to 12 significant digits, with money shown to cents where applicable.
Saved scenario
Save the current answer, then change an input to compare. This clears when you leave.
Formula and assumptions
E[X] = Σxp; Var(X) = Σp(x − mean)². Probabilities must sum to 1 within numeric tolerance; they are never silently normalized. Values may repeat, representing distinct outcomes with equal values.
In a list, use spaces, new lines, semicolons, or commas followed by a space. A comma between groups of three digits is a thousands separator.
Automatic precision shows numbers to 12 significant digits. Thousands separators such as 1,000 are accepted; use a dot for decimals.
Scratch calculator
Use +, −, ×, ÷, parentheses and %. A percentage is divided by 100. This does not change the main tool.
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Updated 
Using Probability distribution calculator
Calculate mean and variance for a discrete distribution with values and probabilities you supply.
E[X] = Σxp; Var(X) = Σp(x − mean)². Probabilities must sum to 1 within numeric tolerance; they are never silently normalized. Values may repeat, representing distinct outcomes with equal values.
Next: Expected value calculator
A worked example
Example inputs: possible values = 0, 10, matching probabilities = 0.8, 0.2. Expected value = 2.
Before you use the result
E[X] = Σxp; Var(X) = Σp(x − mean)². Probabilities must sum to 1 within numeric tolerance; they are never silently normalized. Values may repeat, representing distinct outcomes with equal values.
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ToolOctopus. “Probability distribution calculator.” Updated 2026-09-26. https://tooloctopus.com/probability-distribution-calculator.
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