The Cumulative distribution function F(x) is a ans. Monotonic non-decreasing function Monotonic increasing function Monotonic decreasing function none
Question
The Cumulative distribution function F(x) is a
ans. Monotonic non-decreasing function
Monotonic increasing function
Monotonic decreasing function
none
Solution
The Cumulative Distribution Function (CDF), F(x), is a Monotonic non-decreasing function.
Here's why:
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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.
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Therefore, F(x) is a monotonic non-decreasing function.
It's important to note that F(x) can be a monotonic increasing function if the probability distribution has no flat regions (i.e., regions where the probability density function is zero). However, in general, we can only say that F(x) is a monotonic non-decreasing function.
Similar Questions
The Cumulative distribution function F(x) is a
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