Expected Value(Geometric)

The Geometric Expected Value calculator computes the expected value, E(x), based on the probability (p) of a single random process.

INSTRUCTIONS: Enter the following:

• (p) This is the Single Trial Success Probability

Expected Value: 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

In probability theory, the expected value (or expectation, mathematical expectation, EV, mean, or first moment) refers, intuitively, to the value of a random variable one would "expect" to find if one could repeat the random variable process 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. In other words, each possible value that the random variable can assume is multiplied by its assigned weight, and the resulting products are then added together to find the expected value. The weights used in computing this average are the probabilities in the case of a discrete random variable (that is, a random variable that can only take on a finite number of values, such as a roll of a pair of dice), or the values of a probability density function in the case of a continuous random variable (that is, a random variable that can assume a theoretically infinite number of values, such as the height of a person).

The expected value of a geometric experiment is equal to 1/p which is the number of trials needed to get your first success.

 
[Mike's version] 

This equation computes the expected value (EV) for a randomly generated geometric distribution, given the input probability for a single trial to succeed.

Probability theory described the "expected" value of a a random distribution to correlate to some function we know to show a central tendency to occur frequently or more than other values.  So we often use mean, first moment, or other functions representing a tendency to be close to the center or most dense set of values in the probability distribution. We know for example that a random Gaussian (normal) distribution is very much the same to the left or the tight of the mean and so the mean is ALWAYS the expected value (EV) for a normal distribution.  Other distributions have a skewness to the plus or minus side that must be taken into account when we look for a defining feature of the distribution like its EV.  When we know how to characterize the probability distribution, the EV almost falls out intuitively.  Nevertheless, we try to mathematically define the EV for a number of common probability distributions. 

In this case for a geometric distribution,  if we were to generate a very large set of random values geometrically distributed, like the role of a single six-sided dice, we would find that the EV is precisely 1/p, where p is the probability of success for each trial. In the case of a dice, each trial has a 1 in 6 chance of being the number we want.  Therefore the expected value (EV) for this geometric distribution describing the chances of rolling a chosen value on the dice is 6.