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Cumulative Probability


The cumulative probability of a random variable X at x is

 P(X<=x)=F_X(x),

where F_X is the distribution function. For a continuous random variable with probability density function f_X,

 F_X(x)=int_(-infty)^xf_X(t)dt,

while for a discrete random variable it is the sum of the probabilities of all values not exceeding x.


See also

Distribution Function, Probability Density Function, Random Variable

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References

Ross, S. M. A First Course in Probability, 8th ed. Upper Saddle River, NJ: Pearson, 2010.

Cite this as:

Weisstein, Eric W. "Cumulative Probability." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/CumulativeProbability.html

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