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Questions › IIT JAM › IIT JAM 2023 › Q39
2 marksStatistics › Random variables and standard distributions › Random variables, PMFs, PDFs and CDFsHardabout 3 min

IIT JAM 2023 Question 39: Random variables and standard distributions

Which functions qualify as a cumulative distribution function of a random variable XXX? (A) 1−e−x1-e^{-x}1−e−x on (0,∞)(0,\infty)(0,∞), else 000. (B) (1+e−x)−1(1+e^{-x})^{-1}(1+e−x)−1 on R\mathbb{R}R. (C) 1−x−1ln⁡x1-x^{-1}\ln x1−x−1lnx on (e,∞)(e,\infty)(e,∞), else 000. (D) 1−(ln⁡x)−11-(\ln x)^{-1}1−(lnx)−1 on (e,∞)(e,\infty)(e,∞), else 000.

Select all that apply.

Answer and worked solution

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Plain-text version

Which functions qualify as a cumulative distribution function of a random variable X? (A) 1-e^(-x) on (0,∞), else 0. (B) (1+e^(-x))⁻¹ on ℝ. (C) 1-x⁻¹ln x on (e,∞), else 0. (D) 1-(ln x)⁻¹ on (e,∞), else 0. (A) F(x)=1-e^(-x) on (0,∞), 0 otherwise (B) F(x)=(1+e^(-x))⁻¹ on (-∞,∞) (C) F(x)=1-x⁻¹ln x on (e,∞), 0 otherwise (D) F(x)=1-(ln x)⁻¹ on (e,∞), 0 otherwise

Also written as: Which functions qualify as a cumulative distribution function of a random variable X? (A) 1-e^(-x) on (0, inf), else 0. (B) (1+e^(-x))^(-1) on R. (C) 1-x^(-1)ln x on (e, inf), else 0. (D) 1-(ln x)^(-1) on (e, inf), else 0.

Random variables and standard distributions has come up 173 times in 7 exams since 2005.

What this question tests

This question is on Random variables, PMFs, PDFs and CDFs, part of Random variables and standard distributions in Statistics.

Describing a random variable by its mass, density or distribution function.

TestStop has 33 past-paper questions on this subtopic.

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