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# Cumulative Probability

#### What is Cumulative Probability?

Cumulative probability refers to the likelihood that the value of a random variable is within a given range. For example,

Pr(a ≤ X ≤ b)

Where X is a random variable and a and b are the range limits. Frequently, it is used to calculate the probability that a random variable is less or equal to a specified value:

Pr(X ≤ b)

#### Why is Cumulative Probability Important?

Cumulative probability is a basic concept in statistics and probability theory. It plays an important role in modeling and forecasting. For example, in finance, it is used to predict the likelihood that asset prices will be within a given range. Similarly, it is applied in economics, biology, physics, information science, geology, and several other areas that use random variables in modeling and prediction.

#### Cumulative Probability + LogicPlum

Calculating cumulative probabilities is part of the statistical body of knowledge. Not all modeling practitioners possess this type of knowledge, and thus, many feel limited when applying technologies such as artificial intelligence or machine learning.

LogicPlum’s platform bridges this problem for them through automation. It acts as a source of proven AI research and translates it into practice without human intervention. It works by testing hundreds of models, comparing them based on a performance metric, and selecting the most efficient one. In addition, it provides users with an automatically-generated comprehensive report that explains all the steps taken in the model construction process.

The main advantage of this approach to AI is that users can concentrate on what interest them most: interpreting the model results and forecasting outcomes.

##### Guide to Further Reading

For those interested in knowing the basics of cumulative probability calculation:

Stat Trek. *Statistics Dictionary.* Available at https://stattrek.com/statistics/dictionary.aspx?definition=cumulative_probability