Let's first understand, what is Cumulative Distribution Function (CDF) and it's Definition-

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__What is Cumulative Distribution Function (____CDF)__?

__What is Cumulative Distribution Function (__

__CDF)__?

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__Definition of CDF__-

The Cumulative Distribution Function (CDF) of a random variable 'X' may be defined as the probability that the random variable 'X' takes a value 'Less than or equal to x'.__Definition of CDF__

Mathematically it can be represented as-

CDF Formula |

Cumulative Distribution Function (CDF) may be defined for-

#Continuous random variables and

#Discrete random variables

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**Cumulative Distribution Function (CDF) other Names**

#Probability distribution function of the random variable**Cumulative Distribution Function (CDF) other Names**

#Distribution function of the random variable

#Cumulative probability distribution function

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**
Properties of Cumulative Distribution Function (CDF)**

Following image discusses the 3 Properties of Cumulative Distribution Function (CDF)**Properties of Cumulative Distribution Function (CDF)**

Properties of CDF (Cumulative Distribution Function Properties) |

__Cumulative Distribution Function (CDF) for discrete random variables__

If 'X' is a discrete random variable, then it takes on values at discrete points.__Cumulative Distribution Function (CDF) for discrete random variables__

Therefore CDF can be defined for this case as shown in the image below-

CDF for Discrete Random Variable Explanation |

So the CDF for a discrete random variable for the complete range of x can be defined as shown in the image below-

CDF for Discrete Random Variable |

=> Cumulative Distribution Function (CDF) of a discrete variable at any certain event is equal to the summation of the probabilities of random variable upto that certain event.

As x varies from -∞ to ∞ the graph of CDF i.e. Fx(x) resembles a staircase with upward steps having height P(X=xj) at each x=xj.

But note one thing that the graph of Fx(x) CDF remains constant between the two steps or events.

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