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

No annotations are provided, so the description carries the full behavioral burden, and it discloses nothing: no return value, no domain/range constraints, no error behavior, no unit conventions. For a numeric computation tool this is a complete gap.

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

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

It is short, but this is under-specification rather than concision — the single sentence is a redundant echo of the title with no information front-loaded. There is nothing to trim, but nothing that earns its place either.

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

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

For a statistical function with no annotations, no output schema, and junk parameter text, an agent has insufficient information to invoke it correctly. The description should state what is computed from x and lambda and what is returned.

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

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

Schema description coverage is nominally 100%, but both entries are meaningless placeholders ('X to process', 'Lambda to process') that convey no semantics such as 'x must be >= 0' or 'lambda > 0 is the rate parameter'. The description adds nothing to compensate, so the effective parameter documentation is very weak.

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

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

The description 'Exponential Pdf: Exponential Pdf' is a pure restatement of the tool name with no verb and no explanation of what is computed. An agent cannot tell from this whether it evaluates a probability density at x, fits parameters, or generates samples.

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

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

There is no guidance on when to use this tool, what inputs are valid, or how it relates to siblings such as x402-normal-pdf, x402-binomial-pmf, or x402-poisson-pmf. Nothing routes the agent to or away from it.

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