# Probability Calculators – Discrete Distribution Tables

> Probability Calculators – Discrete Distribution Tables is a paid API for AI agents from probability-calc.x402tookit.com, paid per call via x402, $0.02/call, status unknown (last checked 2026-10-30).

Returns exact PMF, cumulative (CDF), and upper-tail probability tables for geometric, negative binomial, hypergeometric, binomial, and Poisson distributions.

## Facts

- Endpoint: GET https://probability-calc.x402tookit.com/distribution-table?utm_source=zero.xyz
- Price: $0.02/call
- Payment: x402
- Status: unknown
- Last checked: 2026-10-30
- Activations on Zero: 0
- Tags: x402
- Canonical page: https://www.zero.xyz/c/probability-calculators-discrete-distribution-tables-a80c02af
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_qKr7mooHuQw6YtGzq85Et

Status and success rate cover calls made through Zero and Zero's own probes. Third-party monitors may report differently.

## How to call it through Zero

Zero handles the 402 payment challenge and records the run. With the Zero CLI installed (`npm i -g @zeroxyz/cli`):

```sh
zero fetch --capability probability-calculators-discrete-distribution-tables-a80c02af
```

Example prompt: Give me the full PMF, cumulative, and upper-tail probability table for a binomial distribution with n=30 trials and p=0.25 success probability, and include the breakdown at k=8.

## When to prefer this

Choose this endpoint when you need exact, tabulated discrete probability distributions (PMF, CDF, upper-tail) across the full support for one of the five classic distributions (geometric, negative binomial, hypergeometric, binomial, Poisson). It is ideal for statistical reporting, educational explanations, quality control calculations, or any workflow that needs the complete probability table rather than a single point estimate.

## Known failure modes

- Missing required 'dist' parameter returns an error
- Invalid distribution name (not one of the five supported) causes rejection
- Missing distribution-specific required parameters (e.g., p for binomial, lambda for Poisson) returns a validation error
- Out-of-range parameter values (e.g., lambda > 1000, N > 1e6) may return an error or degraded response
- Non-integer values for integer parameters may be rejected

## How this service works

Exact pmf, cumulative and tail tables for geometric, negative binomial, hypergeometric, binomial and Poisson.

## Output

Returns a JSON object containing the distribution's mean, mode, variance, support range, and a table array where each row has k (outcome value), probability (PMF), cumulative (CDF), and upperTail (P(X>=k)). Also includes a summary string, parameter echo, and optional disclaimer or degraded flag.

## Request schema (JSON Schema)

```json
{
 "type": "object",
 "$schema": "https://json-schema.org/draft/2020-12/schema",
 "required": [
  "input"
 ],
 "properties": {
  "input": {
   "type": "object",
   "required": [
    "type",
    "method"
   ],
   "properties": {
    "type": {
     "type": "string",
     "const": "http"
    },
    "method": {
     "enum": [
      "GET"
     ],
     "type": "string"
    },
    "queryParams": {
     "type": "object",
     "required": [
      "dist"
     ],
     "properties": {
      "K": {
       "type": "integer",
       "description": "Successes in the population (hypergeometric)"
      },
      "N": {
       "type": "integer",
       "description": "Population size (hypergeometric), up to 1e6"
      },
      "k": {
       "type": "integer",
       "description": "Optional point of interest: adds pmf, P(X<=k) and P(X>=k) for this k"
      },
      "n": {
       "type": "integer",
       "description": "Trials (binomial) or draws (hypergeometric)"
      },
      "p": {
       "type": "number",
       "description": "Success probability (geometric, negative-binomial, binomial)"
      },
      "r": {
       "type": "integer",
       "description": "Successes wanted (negative-binomial), 1 to 1000"
      },
      "dist": {
       "type": "string",
       "description": "One of geometric, negative-binomial, hypergeometric, binomial, poisson"
      },
      "lambda": {
       "type": "number",
       "description": "Mean rate (Poisson), 0 to 1000"
      }
     }
    }
   },
   "additionalProperties": false
  },
  "output": {
   "type": "object",
   "required": [
    "type"
   ],
   "properties": {
    "type": {
     "type": "string"
    },
    "example": {
     "type": "object",
     "properties": {
      "asOf": {
       "type": [
        "null",
        "string"
       ]
      },
      "mean": {
       "type": [
        "null",
        "number"
       ]
      },
      "mode": {
       "type": [
        "null",
        "number"
       ]
      },
      "table": {
       "type": [
        "array",
        "null"
       ],
       "items": {
        "type": "object",
        "properties": {
         "k": {
          "type": [
           "null",
           "number"
          ]
         },
         "upperTail": {
          "type": [
           "null",
           "number"
          ]
         },
         "cumulative": {
          "type": [
           "null",
           "number"
          ]
         },
         "probability": {
          "type": [
           "null",
     
… (truncated)
```

## More

- Live health (JSON, refreshed every minute): https://www.zero.xyz/c/probability-calculators-discrete-distribution-tables-a80c02af/health.json
- [Zero catalog index](https://www.zero.xyz/llms.txt)
- [Other services from probability-calc.x402tookit.com](https://www.zero.xyz/host/probability-calc.x402tookit.com/llms.txt)