CALCULATE_MCP

calculate_probability

Compute normal PDF/CDF, binomial PMF/CDF, or Poisson PMF/CDF for statistical analysis and probability calculations.

Instructions

Evaluate normal PDF/CDF, binomial PMF/CDF, or Poisson PMF/CDF.

Tool call template

Replace each placeholder with a value matching the input schema. Only required parameters are included; add optional parameters as needed.

{
  "id": 1,
  "jsonrpc": "2.0",
  "method": "tools/call",
  "params": {
    "arguments": {
      "distribution": "<distribution>",
      "operation": "<operation>",
      "params": "<params>"
    },
    "name": "calculate_probability"
  }
}

Input Schema

Name	Required	Description
`params`	Yes	Normal: x, mean?, sd?. Binomial: k,n,p. Poisson: k,lambda.
`operation`	Yes
`distribution`	Yes

Schema Changelog

Changes observed during successful MCP inspections.

First observedv0.2.0Sep 14, 2026

TDQS

C2.9/5.0

Behavior2/5

Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?

No annotations are provided, so the description must carry the full burden. It does not state whether params accept defaults, what happens on invalid inputs, or how results are returned. The only behavioral hint is the enumeration of supported distributions/operations, which is thin for a computational tool.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Conciseness5/5

Is the description appropriately sized, front-loaded, and free of redundancy?

A single, dense sentence that front-loads the operation and lists the supported configurations. No filler.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Completeness2/5

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

For a 3-param computational tool with no annotations, no output schema, and only 33% schema coverage, the description is too terse. It doesn't explain parameter defaults, output format, or edge cases. An agent would likely need to inspect the schema and guess at behavior.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Parameters3/5

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

Schema description coverage is 33%, and the description repeats the distribution list but adds nothing about the params object beyond what the schema's description already says. The schema's params description is actually richer than the tool description. Baseline is 4 when zero params; with 3 params and low coverage, the description fails to compensate, so a 3 is appropriate.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Purpose4/5

Does the description clearly state what the tool does and how it differs from similar tools?

States a specific verb ('Evaluate') and resource (probability distributions, listing normal/binomial/Poisson and the PDF/CDF/PMF forms). Clearly distinguishable from siblings like calculate_matrix or calculate_calculus. It stops short of a 5 because it doesn't say why one would pick this over summarize_statistics.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Usage Guidelines2/5

Does the description explain when to use this tool, when not to, or what alternatives exist?

No guidance on when to use this tool versus the many calculate_* siblings, nor any exclusions. The name and description imply a domain (probability), but the agent receives no explicit routing cue.

Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.

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