What is a probability distribution?

A probability distribution is a mathematical and statistical function that describes the probability of different possible values of a variable. Probability distributions are often depicted using graphs or probability tables.

How to use the MathCalc probability distribution calculator?

1. Choose one distribution type from the drop-down list:
• Poisson
• Exponential
• Uniform
• Gamma
• Beta
• Weibull
• Log-Normal

2. Choose one calculation type from the drop-down list:
• Calculate probability
• Find percentile
• Distribution statistics

3. Enter the lambda-rate parameter.
4. Enter the k (number of events).
5. Enter X values.
6. Enter the minimum value (a).
7. Enter the maximum value (b).
8. Enter the alpha-shape parameter.
9. Enter the Beta-scale/shape parameter.
10. Enter the scale parameter.
11. Enter the shape parameter.
12. Enter the Mu- location parameter.
13. Enter the sigma-scale parameter.
14. Enter the probability (0-1).
15. After entering the values, click “calculate”, and in seconds, you will see the result.

Calculate Probability by choosing Distribution Type “Poisson distribution”

Lambda: 3.5, k: 2
Solution:
P(X=k) = (λ^k * e^-λ) / k!
P(X=2) = 0.184959
Result:
Probability: 0.184959

Calculate Probability by choosing Distribution Type “Exponential probability”

Lambda: 0.2, X value: 5
Solution:
PDF: f(x)=λe^-λx = 0.073576
CDF: F(x)=1-e^-λx = 0.632121
Result:
PDF: 0.073576
CDF: 0.632121

Calculate Percentile by choosing Distribution Type “Uniform Distribution”

Minimum value (a): 10, maximum value (b): 30, probability: 0.25
Solution:
PDF: f(x)=1/(b-a) = 0
CDF: F(x) = 0
Result:
PDF: 0
CDF: 0

Calculate Probability by choosing Distribution Type “Gamma distribution”

X Value=5, Alpha (α) = 3, Beta (β) = 2
Solution:
PDF: f(x) = x^(α-1) * e^(-x/β) / [Γ(α) * β^α] = 0.128258
Result:
PDF: 0.128258

Calculate Probability by choosing Distribution Type “Beta distribution”

Alpha (α) = 2, Beta (β) = 5, X Value = 0.6
Solution:
PDF: f(x) = x^(α-1) * (1-x)^(β-1) / B (α, β) = 0.4608
Result:
PDF: 0.4608

Calculate Percentile by choosing Distribution Type “Weibull distribution”

Shape: 1.5, Scale: 20, Probability: 0.9
Solution:
PDF: f(x) = (k/λ) *(x/λ)^(k-1) * e^(-(x/λ)^k) = 0
Result:
PDF: 0

Calculate Probability by choosing Distribution Type “Log-Normal distribution”

Mu (μ) = 0, Sigma (σ) = 1, X Value = 2.5
Solution:
PDF: f(x) = (1 / (xσ√2π)) * e^(-(lnx - μ)^2 / (2σ^2)) = 0.104871
Result:
PDF: 0.104871

Why use the MathCalc probability distribution calculator?

Get Quick Results

If you are finding Poisson distribution, Exponential distribution, Uniform distribution, Gamma distribution, Beta distribution, Weibull distribution, or log-Normal distribution by hand, it can be time-consuming, especially when dealing with large values. This MathCalc Probability distribution calculator gives you accurate results in seconds.

Reduce Human Error

Manual math can lead to minor mistakes that cost you money or points. This tool provides proven formulas to reduce errors, and your results are always right. To avoid miscalculations, use the MathCalc Probability calculator.

User Friendly

This free Probability distribution calculator calculates probability, finds the percentile, and distribution statistics. This calculator is helpful for students and teachers.

Tips for Best Results:

• Enter probability as a decimal between 0 and 1.
• Used the correct field names for each distribution.
• Always double-check your inputs.

FAQ

What is the difference between PDF/PMF and CDF?

PMF/PDF gives the height at a point; CDF gives the cumulative probability up to that point. Probabilities for continuous distributions come from areas (CDF differences), not from PDF heights.

When should I use “probability (0-1)”?

Use it in the Find percentile mode. Enter values like 0.1, 0.5, 0.95 to get the 10th, 50th, or 95th percentile.