1. What is Distribution Probability?

The probability that a random variable takes on a value within a specified range is given by the integral of its probability density function (PDF) over that range. This fundamental concept in statistics helps quantify uncertainty and model random phenomena.

2. How Does the Calculator Work?

The calculator computes the probability using the integral:

Where:

• \( P \) — Probability of the variable falling between a and b
• \( f(x) \) — Probability density function of the chosen distribution
• \( a \) — Lower bound of the interval
• \( b \) — Upper bound of the interval

3. Types of Distributions

Normal Distribution: Symmetric bell-shaped curve defined by mean and standard deviation.
Uniform Distribution: Constant probability between two bounds.
Exponential Distribution: Models time between events in a Poisson process.

4. Using the Calculator

Steps: Select distribution type, enter bounds, and provide additional parameters as needed (mean, standard deviation). The calculator will compute the probability.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between PDF and CDF?
A: PDF gives probability density at a point, while CDF gives cumulative probability up to a point.

Q2: Can I calculate probabilities for other distributions?
A: This calculator handles common distributions. For others, specialized tools may be needed.

Q3: Why is my probability greater than 1?
A: Probabilities range from 0 to 1. If you see values >1, check your inputs as PDFs can have values >1 but probabilities cannot.

Q4: How accurate are the calculations?
A: The normal distribution uses an approximation with error < 7.5×10⁻⁸. Other distributions use exact formulas.

Q5: What if my lower bound is greater than upper bound?
A: The calculator will automatically swap them and give the correct probability.