How to find cdf from pdf

Written by shannon johnson
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How to find cdf from pdf
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PDF stands for probability density function while CDF stands for cumulative distribution function. The CDF can be found by integrating the PDF based on known properties of both functions. PDF is defined using p(x) and CDF is defined using P(x). In this case, P(x) is an anti-derivative of p(x).

Skill level:
Moderate

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Things you need

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Instructions

  1. 1

    Take your PDF in the form p(x) on the domain {a,b} and integrate the function to find the CDF function of P(x).

  2. 2

    Solve for the constants of integration using the known properties of P(x). Those are that the function, P(x), goes to one as x approaches infinity and goes to zero as x approaches negative infinity. Further, the function is continuous though not necessarily smooth, and is never decreasing.

  3. 3

    Set up the equation for P(x) so that P(a) equals zero and P(b) equals one and solve for your constants of integration.

  4. 4

    Replace your constants of integration with your solutions from Step 3, and you have your CDF.

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