Intro to Business Statistics

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Probability density function

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Intro to Business Statistics

Definition

A probability density function (PDF) describes the likelihood of a continuous random variable taking on a particular value. It is represented by a curve where the area under the curve within a given interval represents the probability that the variable falls within that interval.

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5 Must Know Facts For Your Next Test

  1. The total area under the curve of a PDF is always equal to 1, representing 100% probability.
  2. A PDF can never take on negative values; it must be non-negative for all possible values of the random variable.
  3. The probability that a continuous random variable exactly equals any specific value is zero; probabilities are only meaningful over intervals.
  4. The integral of a PDF over an interval $[a, b]$ gives the probability that the variable falls within that interval: $P(a \leq X \leq b) = \int_{a}^{b} f(x) \, dx$.
  5. Common examples of PDFs include the normal distribution, exponential distribution, and uniform distribution.

Review Questions

  • What does the area under the curve of a probability density function represent?
  • Can a PDF take on negative values? Explain your answer.
  • How do you calculate the probability that a continuous random variable falls within an interval $[a, b]$ using its PDF?

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