About Probability Distribution Calculator (Continuous & Discrete)
Comprehensive statistical distributions laboratory. Computes probability density functions (PDF / PMF), cumulative distribution functions (CDF: P(X ≤ x)), survival functions (P(X > x)), and expected values for Normal, Student’s t, Chi-Square, Binomial, Poisson, and Exponential distributions.
Key Capabilities & Features
- Six fundamental distributions: Normal, Student’s t, Chi-Square, Binomial, Poisson, and Exponential
- Dual probability evaluation: Point density / mass (PDF / PMF) and cumulative area (CDF)
- Survival function calculation: P(X > x) for reliability and survival analysis applications
- Theoretical summary metrics: Exact expected value E[X] and theoretical variance Var(X)
- Dynamic distribution curve rendering with shaded cumulative probability region
How to Use Probability Distribution Calculator (Continuous & Discrete)
Select Distribution Family
Choose your desired continuous or discrete distribution.
Configure Distribution Parameters
Enter parameters such as mean and standard deviation, degrees of freedom, or rate λ.
Specify Evaluation Value x
Type the threshold value x to evaluate.
Inspect Probabilities
Read CDF cumulative probability P(X ≤ x), survival P(X > x), and point density.
Privacy & In-Browser Execution Guarantee
100% Client-Side. All probability integrals and special functions compute locally in browser memory.
Frequently Asked Questions
What is the distinction between PDF and CDF?
A Probability Density Function (PDF) represents the relative likelihood of a continuous random variable taking a specific value, while the Cumulative Distribution Function (CDF) measures the probability that X is less than or equal to x.
Why is the PDF of a continuous variable not a probability?
For continuous variables, the probability of any single exact point is zero; probabilities are defined over intervals, representing the area under the PDF curve.