Use this probability or sampling tool to compute a stated quantity or generate reproducible draws from a precisely parameterized distribution or stochastic model.

Values

Required list input.

Probabilities

Required list input.

Calculate the probability-weighted expected value of discrete outcomes. The tool evaluates the supplied inputs together and returns the named outputs below; it does not infer omitted operating conditions or change the units shown.^[1]

Expected value

The resulting expected value returned as a number.

• Results depend on parameterization, support, random source, seed, convergence, burn-in, autocorrelation, proposal quality, normalization, numerical tails, and whether model assumptions match the process. Samples are not exact evidence of convergence.
• Use finite inputs in the displayed units and preserve more precision than the final presentation requires. Independently verify safety-critical, financial, compliance, or production decisions.

Check analytic moments or known test cases, use independent chains and diagnostics for Monte Carlo methods, report seed and effective sample size, and inspect tail behavior.

• Probability Complement Calculator

  Calculate the complement of a probability.

• Empirical Probability Calculator

  Calculate empirical probability from observed successes and trials.

• Discrete Importance Sampler

  Draw category indices from a proposal distribution and return target/proposal importance weights; proposal support must cover every positive target category.