⏳ Exponential Distribution Calculator
Calculate waiting-time probabilities for a continuous exponential distribution.
📊 Statistics📐 Formula included🧠 Practice questions✓ Free
Please enter valid values.
Formula and Explanation
Calculate waiting-time probabilities for a continuous exponential distribution.
| Concept | Formula or rule |
|---|---|
| Exponential Distribution Calculator | F(x) = 1 − e⁻ˡᵃᵐᵇᵈᵃˣ · S(x)=e⁻ˡᵃᵐᵇᵈᵃˣ |
How to Use This Calculator
- Enter the sample, counts, probabilities, or summary statistics requested above.
- Keep paired lists in the same order and separate values with commas.
- Select the correct test direction or sample/population option when available.
- Press Calculate and interpret the result together with the supporting statistics.
Worked Example
Example: With λ=0.2 per minute, the mean waiting time is 1/0.2=5 minutes.
✓ P(X≤5)=1−e⁻¹≈0.6321
Where This Is Used
School & coursework
Check homework, understand formulas, and verify step-by-step statistics exercises.
Research
Explore estimates, uncertainty, distributions, and relationships before using full statistical software.
Business & data analysis
Summarize variation, compare groups, and communicate data-driven findings clearly.
Common Mistakes to Avoid
⚠️
Confusing rate with mean
Mean waiting time equals 1/λ.
Mean waiting time equals 1/λ.
⚠️
Mixing time units
If λ is per hour, x must be in hours.
If λ is per hour, x must be in hours.
⚠️
Using it when hazard changes strongly over time
The exponential model assumes a constant rate.
The exponential model assumes a constant rate.
Practice Questions
1. If λ=0.5, what is mean waiting time?
Answer: 2
2. What is survival at x=0?
Answer: 1
3. Can x be negative?
Answer: No.
Frequently Asked Questions
Is the exponential distribution memoryless?▾
Yes.
What is its mean?▾
1/λ.
What is its variance?▾
1/λ².