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Probability Density

By Jim Frost

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A probability density describes how probability is distributed over the possible values of a continuous random variable. A probability density function (PDF) is the curve that shows how the density changes across values (see graph below). The probability density at a specific value is the height of the curve at that point.

Unlike discrete probabilities, the probability density at a specific value is not the probability that the variable equals that value. For continuous variables, the probability of any exact value is always zero. Instead, the density tells you how much probability is packed per unit around that value. To calculate the probability of falling within a range of values, you integrate the density over that range.

For a continuous variable like IQ score, the probability density at 100 tells you how tightly probability is concentrated around that IQ point. This density is just one of an infinite number of points along the PDF curve, and the probability of having exactly an IQ of 100 is zero. To get an actual probability, you need to look at a range, like between IQ scores of 95 and 105.

Probability distribution plot of IQ scores.

Related

Related Articles:
  • Probability Density Function: Definition & Uses
  • Probability Density Function: Definition & Uses
  • Cumulative Distribution Function (CDF): Uses, Graphs & vs PDF
  • Probability Mass Function: Definition, Uses & Example
  • Random Variable: Discrete & Continuous
  • Marginal Probability: Definition, Formula & Examples
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