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# How Probability Distributions Work

Perhaps the most common probability distribution is the normal distribution, or “bell curve,” although several distributions exist that are commonly used. Typically, the data generating process of some phenomenon will dictate its probability distribution. This process is called the probability density function.

Probability distributions can also be used to create cumulative distribution functions (CDFs), which adds up the probability of occurrences cumulatively and will always start at zero and end at 100%.

Academics, financial analysts and fund managers alike may determine a particular stock’s probability distribution to evaluate the possible expected returns that the stock may yield in the future. The stock’s history of returns, which can be measured from any time interval, will likely be composed of only a fraction of the stock’s returns, which will subject the analysis to sampling error. By increasing the sample size, this error can be dramatically reduced.

### KEY TAKEAWAYS

• A probability distribution depicts the expected outcomes of possible values for a given data generating process.
• Probability distributions come in many shapes with different characteristics, as defined by the mean, standard deviation, skewness, and kurtosis.
• Investors use probability distributions to anticipate returns on assets such as stocks over time and to hedge their risk.