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FRM Part I · FRM Exam Part I · Random Variables

For a continuous random variable with a strictly increasing CDF F, which statement about the quantile function (inverse CDF) is correct?

The quantile function returns the value x for which the cumulative probability equals p, that is F(x) = p. Because the CDF is strictly increasing, its inverse is also increasing, and the 0.5 quantile is the median, not necessarily the mean.

  1. AF⁻¹(0.5) is the mean of the distribution
  2. BF⁻¹(p) returns the value x such that F(x) = pCorrect
  3. CF⁻¹(p) returns the density at probability p
  4. DF⁻¹(p) is decreasing in p

Explanation

The quantile function maps a probability p to the x with F(x) = p. The median F⁻¹(0.5) equals the mean only for symmetric distributions. Since F is increasing, its inverse is increasing, and it returns a value, not a density.

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