Suppose is a density function for a certain distribution and is the cumulative distribution function for the same distribution. Which of the following gives the fraction of the distribution between x = 7 and x = 16? Select all that apply.

Question

Suppose  is a density function for a certain distribution and  is the cumulative distribution function for the same distribution. Which of the following gives the fraction of the distribution between x = 7 and x = 16? Select all that apply.

Quizplus · Accepted Answer

To find the fraction of the distribution between x = 7 and x = 16, we need to calculate the value of the cumulative distribution function (CDF) at x=16 and subtract the value of the CDF at x=7 from it.

Fraction of distribution between x=7 and x=16 = CDF(16) - CDF(7)

Substituting the given CDF 11eb69ff_fe20_ee7d_af94_4745a9054756_TB8190_11 in the above formula, we get:

Fraction of distribution between x=7 and x=16 = 11eb69ff_fe21_158f_af94_3ff524d4ad94_TB8190_11 - 11eb69ff_fe21_1590_af94_eb712e782f98_TB8190_11

Simplifying the above expression, we get:

Fraction of distribution between x=7 and x=16 = 11eb69ff_fe20_ee7e_af94_978a2f8683ba_TB8190_11

Therefore, option A is correct. However, the question asks us to select all the correct options. On closer inspection, we can see that options B and C are identical to the difference between CDFs we calculated above. Therefore, both B and C are also correct options. Option D is not correct as it is the value of the density function at x=16, and we need to use the CDF instead to calculate the fraction of the distribution between x=7 and x=16.

Suppose Is a Density Function for a Certain Distribution