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The Cumulative Distribution Function (CDF) refers to a statistical concept that describes the probability distribution of a random variable. It represents the probability that a random variable takes on a value less than or equal to a specific value.
The calculator uses the formula:
Where:
Explanation: This formula calculates the Cumulative Distribution Function by multiplying the average duration of fade by the normalized link capacity ratio.
Details: The Cumulative Distribution Function is crucial in probability theory and statistics as it provides a complete description of the probability distribution of a random variable. It is used in various fields including telecommunications, engineering, and data analysis to understand and model random phenomena.
Tips: Enter the average duration of fade in seconds and the normalized LCR value. Both values must be positive numbers greater than zero.
Q1: What does the Cumulative Distribution Function represent?
A: The CDF represents the probability that a random variable takes on a value less than or equal to a specific value, providing a complete description of its probability distribution.
Q2: How is CDF different from PDF?
A: While the Probability Density Function (PDF) describes the relative likelihood of a random variable taking on a given value, the CDF gives the cumulative probability up to that value.
Q3: What are the properties of a CDF?
A: The CDF is always non-decreasing, right-continuous, and approaches 0 as the variable approaches negative infinity and 1 as it approaches positive infinity.
Q4: In what fields is CDF commonly used?
A: CDF is widely used in statistics, probability theory, telecommunications, signal processing, risk assessment, and various engineering disciplines.
Q5: Can CDF be used for both discrete and continuous random variables?
A: Yes, the CDF is defined for both discrete and continuous random variables, though its mathematical properties differ slightly between the two cases.