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The probability cumulative distribution function must be monotone and

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The probability cumulative distribution function must be monotone and

(a) Increasing

(b) Decreasing

(c) Non-increasing

(d) Non-decreasing

I have been asked this question during an interview for a job.

This intriguing question comes from The Z-transform Analysis of Sampled-Data Control Systems in section Digital Control Systems of Control Systems

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Correct answer is (d) Non-decreasing

Easy explanation: The cumulative distribution function that is monotone and non-decreasing or can be increasing.

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