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Probability

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Calculus II

Definition

Probability measures the likelihood of an event occurring, expressed as a number between 0 and 1. It is a fundamental concept in both pure and applied mathematics, often used to model uncertainty.

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5 Must Know Facts For Your Next Test

  1. Probability can be calculated using improper integrals when dealing with continuous random variables.
  2. The probability density function (PDF) must integrate to 1 over its entire range.
  3. The cumulative distribution function (CDF) gives the probability that a random variable is less than or equal to a certain value.
  4. In some cases, improper integrals are used to find the expected value (mean) or variance of a probability distribution.
  5. Understanding convergence of improper integrals is crucial for evaluating probabilities in unbounded intervals.

Review Questions

  • What role do improper integrals play in calculating probabilities for continuous random variables?
  • How do you use the PDF and CDF in evaluating probabilities?
  • Why is it important for the PDF to integrate to 1 over its entire range?
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