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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
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Solution

The Cumulative Distribution Function (CDF), F(x), is a Monotonic non-decreasing function.

Here's why:

  1. 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.

  2. 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.

  3. 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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