Probability Distribution Calculator: Exponential, Geometric, Hypergeometric and Uniform

Four more distributions that come up in statistics courses.

Calculated from standard textbook formulas, with every step shown. The formulas are fixed, so the working does not need checking: what matters is the numbers you type in. Use these calculators only if you are competent to choose the inputs (loads, material strength, dimensions, supports) and check your units and assumptions. For learning and checking your own working: design and sign-off are for a qualified engineer. Drafting Central does not store the numbers you type.

How this calculator works

Choose the distribution.

Enter its parameters and the value you want a probability for.

The calculator gives the probabilities, the mean and the standard deviation.

Formulas used

  • P(X \le x) = 1 - e^{-\lambda x}
  • P(X = k) = (1 - p)^{k-1}p
  • P(X = k) = \frac{\binom{K}{k}\binom{N-K}{n-k}}{\binom{N}{n}}
  • f(x) = \frac{1}{b - a}

Worked example

With the default numbers in the calculator above:

  1. Density at x: 0.111565
  2. Chance that X is at most x: 0.77687
  3. Chance that X is more than x: 0.22313
  4. Mean: 2
  5. Standard deviation: 2
  6. Median: 1.38629

Change the numbers in the calculator to see the full working, every step, for your own case.

A second worked example

A different case, with these numbers: Distribution Geometric (trials until the first success).

  1. Chance of the first success on trial k: 0.1024
  2. Chance of the first success by trial k: 0.5904
  3. Chance it takes more than k trials: 0.4096
  4. Mean number of trials: 5
  5. Standard deviation: 4.47214

Common questions

When do I use the exponential distribution?

For the waiting time between random events that happen at a steady average rate, such as the time between calls to a help desk.

What is the difference between the hypergeometric and the binomial?

The binomial is for sampling with replacement or from a very large population. The hypergeometric is for sampling without putting the items back.

What does the geometric distribution count?

The number of trials up to and including the first success.

Related calculators

Got a question about this? Ask an engineering question and get a plain-language answer with references.

Further reading: Any probability and statistics text (standard probability distributions).

Need a calculator we do not have?

Tell us what you would like to calculate. We read every request and build the most asked-for ones.

We store your request (and your email if you give it) to decide what to build. We do not store the numbers you type into calculators.

Embed this calculator on your own page

Copy this code into your page. The calculator runs inside the frame and links back to Drafting Central.

Need this drawn, designed or checked?

Drafting Central is a mechanical engineering and drafting business working with customers across Australia and around the world. A calculator gives you the numbers; we can turn them into drawings and designs.

Need help with a real project?

Talk to Drafting Central →

← All engineering calculators