Question on the maximum probability of CDF?

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SUMMARY

The maximum probability value of a cumulative density function (CDF) is definitively 1. This is because a CDF represents the probability of a random variable being less than or equal to a certain value, and probabilities are constrained between 0 and 1. In contrast, a probability density function (PDF) can take on arbitrarily large values, provided that the integral of the PDF equals 1. Probability mass functions (PMFs) also adhere to the same constraint as CDFs, remaining less than or equal to 1.

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  • Understanding of cumulative density functions (CDFs)
  • Knowledge of probability density functions (PDFs)
  • Familiarity with probability mass functions (PMFs)
  • Basic concepts of probability theory
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Statisticians, data analysts, and students of probability theory seeking to clarify the concepts of cumulative density functions and their properties.

holymackerel
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Hi guys, i would like if people can tell what is the maximum probability value that a cumulative density function (cdf) can have?

i have been confused by the definition... however i have come to think that the maximum will be 1.. because all events can only be between 0 to 1 (100%) chance... however some told me that it could be infinite... can anyone clarifty it?
 
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The cdf does indeed top out at 1. A pdf, however, can have arbitrarily large values; it just has to integrate to 1. The same is not true of a probability mass function, which is again always less than or equal to 1.
 

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