{"uid":"cap_OZkmZDJ0mj77fIi_3jmcA","slug":"poisson-distribution-calculator-fc55c9bb","name":"Poisson Distribution Calculator","description":"Kostenlose Guides, Solo-Playbooks und Artikel zu KI, Automation und Side Hustles — für Menschen, die mit echten Systemen online Einkommen aufbauen wollen. Transparent finanziert über faire Affiliate-Links.","url":"https://kihustle.tech/api/v1/poisson-distribution","method":"POST","headers":{},"bodySchema":{"type":"object","properties":{"k":{"type":"integer"},"lambda_rate":{"type":"number"}}},"responseSchema":{"type":"json","example":{"result":"processed","status":"success"}},"example":null,"exampleRequest":null,"tags":["x402"],"displayCostAmount":"0.002","displayCostAsset":"USDC","priceDynamic":false,"priceHint":null,"priceStatus":"priced","priceSource":"probe","requiresHandshake":false,"reviewCount":0,"rating":{"score":"0.00","successRate":"0.00","reviews":0,"stars":null,"state":"unrated"},"availabilityStatus":"unknown","priceObserved":null,"sessionDeposit":null,"pricing":{"kind":"static","summary":"$0.002/call","primary":{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.002","per":"call","confidence":"exact"},"accepted":[{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.002","per":"call","confidence":"exact"}]},"paymentMethods":[{"uid":"pm_Mp3dISV1sXonoY7cN-u-B","protocol":"x402","methodType":"crypto","chain":"base","mode":"charge","costAmount":"0.002","costPer":"request","priority":0,"asset":"0x833589fCD6eDb6E08f4c7C32D4f71b54bdA02913","unit":"request","depositMicros":null,"planRef":null}],"brandName":null,"brandSlug":null,"brandBaseUrl":null,"brandDocsUrl":null,"whatItDoes":"Computes the Poisson probability mass function P(X=k) given an event rate (lambda) and a count (k)","exampleAgentPrompt":"What is the Poisson probability of exactly 3 events occurring if the average rate is 2.5 events per interval?","exampleUseCases":[{"title":"Call center traffic modeling","prompt":"Given that our call center receives an average of 5 calls per minute, what's the probability that exactly 7 calls arrive in a given minute?"},{"title":"Website error rate analysis","prompt":"Our server averages 1.2 errors per hour — what's the Poisson probability of getting exactly 0 errors in the next hour?"},{"title":"Quality control defect estimation","prompt":"If a production line produces on average 2 defects per batch, what's the probability of seeing exactly 4 defects in a single batch?"}],"resultDescription":"Returns a JSON object with a computed Poisson probability result and a success status indicator, representing P(X=k) for the given lambda_rate and k values.","failureModes":["Missing or non-integer k value returns an error","Negative lambda_rate may cause computation failure","Malformed JSON body results in a 400-level error","Very large k values may cause numerical overflow","Payment not included or invalid returns a 402 response"],"whenToPreferThis":"Use this endpoint when you need a quick, pay-per-call Poisson PMF computation without setting up a local math library or stats environment. Best suited for agents performing probabilistic modeling of rare or discrete events (arrivals, defects, failures) where k and lambda are already known.","instructions":null,"reviewSummary":null,"reviewSummaryHighlights":null,"reviewSummaryConcerns":null,"reviewSummaryGeneratedAt":null,"activationCount":0,"lastUsedAt":null,"lastSuccessfullyRanAt":null,"lastHealthCheckAt":"2026-09-13T19:01:40.104Z","isFirstParty":false}