The Cumulative distribution function F(x) is a ans. none Monotonic non-decreasing function Monotonic increasing function Monotonic decreasing function
Question
The Cumulative distribution function F(x) is a
- ans.
- none
- Monotonic non-decreasing function
- Monotonic increasing function
- Monotonic decreasing function
Solution
The Cumulative Distribution Function (CDF), F(x), is a Monotonic non-decreasing function.
Here's why:
-
The CDF, F(x), of a random variable X is defined as the probability that X will take a value less than or equal to x.
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As we increase the value of x, the set of outcomes where X is less than or equal to x can only increase or stay the same. This means that the probability F(x) can only increase or stay the same as x increases.
-
Therefore, F(x) is a monotonic non-decreasing function.
Note: While F(x) is always non-decreasing, it is not always strictly increasing. For example, if there is a range of values where the probability density function is zero, then the CDF will be constant over that range.
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