Formula applied.
AskSia uses the Poisson pmf with substitution shown.
Direct
EN
Poisson Distribution Solver
Poisson probabilities, the formula applied step by step.
Type or photograph the rate (lambda) and the count (k) of events. AskSia applies the Poisson pmf, computes the probability, and answers cumulative or range questions.
Works with word problems, equations, code, and science prompts.
∫ 3x² · sin(x) dx
SubjectsCalculusAlgebraPhysicsChemistryBiologyCSStatisticsEcon
4.9 / 5 · trusted by 2M+ students · 50M+ problems solved
asksia.ai/solver
98% · Verified
Problem
Find the area enclosed between y = x² and y = 2x in the first quadrant.
1
Find the points of intersection
Set the curves equal: x² = 2x → x(x - 2) = 0, so x = 0 and x = 2.
2
Identify which curve is on top
On (0, 2), 2x > x², so y = 2x is the upper curve.
3
Set up the area integral
A = ∫₀² (2x - x²) dx
4
Integrate term-by-term
A = [ x² - x³/3 ]₀²
Final Answer
A = 4/3 sq. units
Quick Answer
What is the Poisson distribution?
The Poisson distribution models the number of events occurring in a fixed time or space interval, given that events occur at a constant average rate lambda and are independent. The probability of exactly k events is lambda to the k times e to the negative lambda divided by k factorial. The mean and variance both equal lambda. Common applications: arrivals at a service desk per hour, defects per unit area, rare disease cases per population per year. The Poisson approximates the binomial when n is large and p is small.
98%
solution accuracy
50M+
problems solved
~1.5s
avg solve time
A+
study-ready explanations
Why AskSia Solver
Why students use AskSia for Poisson Distribution.
Every step transparent, every answer self-checked.
Cumulative and tail probabilities.
P(X at most k), P(X at least k), P(a at most X at most b) all computed.
Cumulative
Mean and variance.
Both equal lambda. AskSia confirms.
Properties
Binomial approximation.
When binomial has large n and small p with n times p equal to lambda, the Poisson approximates.
Approximation
Photo, paste, or type.
Snap handwritten or printed problems with your phone, paste from any online homework portal, or type with full LaTeX support.
Multi-modal input
Verified by AskSia.
Every answer gets a self-check pass. Sia catches sign errors and algebra mistakes before you submit your homework.
Self-checked
How It Works
Solve any Poisson Distribution problem in three steps.
Step 01
Enter the problem.
Type the expression, paste from your homework, snap a photo, or speak it. AskSia parses your input and identifies the structure.
Input mode
Snap a Photo
Textbook, handwriting, screenshot
Paste Text
Word problem or equation
Calculator
LaTeX-ready equation editor
Step 02
AskSia picks the method.
Based on the problem structure, AskSia chooses the cleanest solution path and labels each step with the operation performed.
1
Set curves equal
x² = 2x → x = 0, x = 2
2
Set up the integral
A = ∫₀² (2x - x²) dx
3
Evaluate
A = [x² - x³/3]₀² = 4/3
Step 03
Read the verified answer.
Final result appears with a substitution or composition check. Practice problems on the same concept are one tap away.
Auto-generated diagram
Region between y = 2x and y = x² — area = 4/3
Available On
Solve anywhere
you study.
Every solve syncs across Web, iOS, and Android — start it at your desk, finish on your phone.
Web App
Full study studio
Split-panel interface with the worked solution on the left, the auto-generated diagram and AI tutor chat on the right.
Drag & drop image upload + LaTeX equation editor
Auto-generated diagrams render alongside steps
Side-panel AI tutor chat for hints and alt methods
Export to PDF, DOCX, Notion, or Google Docs
Hi! What are we studying today?
Ask about your homework, lecture, or readings...↑
Calculus
98% verified
1.4s
Step 4 of 4 · Evaluate
A = [x² - x³/3]₀² = 4/3
Mobile App
Snap & solve, anywhere
Open the camera, frame the problem, and the worked solution plus diagram appear in seconds.
One-tap snap-and-solve on iOS and Android
Pinch-to-zoom diagrams, swipe between steps
Auto-sync solves with your Web library
Offline review of saved solutions and flashcards
☰
AskSia
+What can I do for you?
Homework solver
Live transcribe
File summary
Snap
YouTube
Flashcard
Calc
98%
1.4s
Area between y=2x & y=x²
A = 4/3 sq. units ✓
Use Cases
What the Poisson Distribution solver covers.
Number of arrivals.
Cars at an intersection per minute, customers at a store per hour.
Arrival
Defects in production.
Defects per square meter of fabric, typos per page.
Defects
Rare events.
Earthquakes, mutations, accidents over a fixed period.
Rare
Modeling counts in biology.
Mutations, bacteria in a sample.
Biology
Approximation of binomial.
When binomial parameters fit, Poisson is a clean stand-in.
Approximation
Verify your homework.
Paste your candidate answer and the original problem. AskSia walks the work, flags any divergent step, and tells you the correct final value.
Answer check
Compare
AskSia vs. ChatGPT,
Photomath & Symbolab.
General chatbots hallucinate. Photo solvers stop at math. AskSia is built for actual coursework with verified accuracy, visual learning, and every subject.
| Feature | AskSia Solver | ChatGPT | Photo Solvers |
|---|---|---|---|
| Solution accuracy | ✓ 98% | ~70-85%, hallucinations | ~90%, math only |
| Auto-generated diagrams | ✓ Every solve | Inconsistent / broken | Graphs only, math-only |
| Step-by-step explanations | ✓ Numbered + plain English | Inconsistent depth | ✓ Math steps |
| Subject coverage | ✓ Math, Physics, Chem, Bio, CS, Econ | ✓ Wide but unverified | Math only |
| Photo input | ✓ Handwriting + diagrams + code | Photos OK, weak on handwriting | ✓ Math photos only |
| Answer verification | ✓ Self-checked before display | No verification | Math engine only |
| Tutor follow-ups | ✓ Hints, alt methods, ELI5 | ✓ General chat | Not available |
| Practice and flashcards | ✓ One-tap from any solve | Manual prompting | Not available |
| Code debugging | ✓ Python, Java, C++, SQL... | ✓ Yes | Not available |
| Free to start | ✓ Daily solves, no card | Limited model access | Steps locked behind paywall |
FAQ
Frequently asked questions.
What does lambda represent?
Lambda is the average rate of events in the chosen time or space interval. If arrivals at a service desk happen at 3 per hour on average, lambda equals 3 for a one-hour window. Lambda must be positive but can be any positive real number, not just an integer. AskSia handles non-integer lambdas naturally.
How is the cumulative probability computed?
Cumulative probability is computed by summing the point probabilities from 0 up to k. For large k, AskSia uses a recursion or normal approximation for efficiency. The complement (P at least k) is computed as 1 minus P at most k minus 1.
Is the Poisson always a good model for counts?
It is a good model when events are independent and occur at a constant average rate. When events cluster (more events when there has been a recent event, like aftershocks of an earthquake), the Poisson is too thin in its tails; you would need a more flexible distribution like the negative binomial.
When does the binomial approximate to Poisson?
When n is large and p is small, with n times p moderate. The binomial pmf approaches the Poisson pmf in the limit. This is useful when binomial computations get heavy: the Poisson is faster to compute and the approximation is excellent for n at least 20 and p at most 0.05.
How accurate is AskSia?
AskSia hits 98% accuracy on standard high school and college coursework, measurably higher than ChatGPT, Photomath, and Symbolab on the same problem sets. Accuracy comes from subject-specialized models, a symbolic verification pass that catches arithmetic errors, and a self-check step that re-derives the answer before showing it to you.
Can I get practice problems and flashcards?
Yes. After any solve, ask Sia to generate similar practice problems at SAT, ACT, AP, IB, or college difficulty, or build a flashcard set on the underlying concept in one tap. Useful for exam prep and spaced repetition before a quiz, midterm, or final.
How much does AskSia cost?
AskSia has a free plan that includes daily solves across all subjects. AskSia Pro and Super include unlimited solves, advanced subjects, the full AI tutor companion, exports, and priority response speed. See pricing for details.
Start Today
Lambda, k, the formula, the probability.
Join 2M+ students using AskSia to solve poisson distribution problems step-by-step. Photo input, plain-English explanations, and a verification check on every solve.