The Pascal Distribution Expected Value calculator computes the expected value based on the success rate (p) and the desired number of successes (r).

INSTRUCTIONS: Enter the following:

• (p) This is the success rate
• (r)  This is the number of successes.

Expected Value E(x): The calculator returns the expected value.

Related Calculators:

• Pascal Distribution Expected Value
• Geometric Expected Value
• Binomial Distribution Expected Value
• Bernoulli Distribution Expected Value
• Geometric Distribution Expected Value
• Discrete Uniform Expected Value
• Hyper-geometric Distribution Expected Value

The Math / Science

This equation computes the mean, or expected value `E(X)` of a Pascal Distribution. The Pascal Distribution is a special case of the negative binomial distribution in which the stopping time parameter, r is an integer.

The inputs to this computation of the Expected Value (mean) are:

• p - the probability of success or success rate for each experimental trial
• r - the number of failures after which we stop the experimental process

The random number of successes,  X, fall within the distribution NB(r;P) such that average number of success, the mean of the distribution,  is 

E(x) = (r*p ) / (1- p)

Notes

In probability theory, the expected value (or expectation, mathematical expectation, EV, mean, or first moment) refers, to the value one would "expect" to find if one could repeat measurement of a random variable an infinite number of times and take the average of the values obtained. More formally, the expected value is a weighted average of all possible values.  This weighted average can be estimated using this equation.