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Questions › DSE › DSE 2015 › Q14
1 mark, −0.333333333333333Statistics › Random variables and standard distributions › Random variables, PMFs, PDFs and CDFsHardabout 4 min

DSE 2015 Question 14: Random variables and standard distributions

Let F:R→RF:\mathbb{R}\to\mathbb{R}F:R→R be a distribution function and define b(c)=inf⁡F−1([c,1])b(c)=\inf F^{-1}([c,1])b(c)=infF−1([c,1]) for c∈(0,1]c\in(0,1]c∈(0,1] (and b(0)=0b(0)=0b(0)=0). If FFF has a jump at xxx, say c=F(x)>a≥F(x−)c=F(x)>a\ge F(x-)c=F(x)>a≥F(x−), then

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Let F:ℝ→ℝ be a distribution function and define b(c)=inf F⁻¹([c,1]) for c∈(0,1] (and b(0)=0). If F has a jump at x, say c=F(x)>a≥ F(x-), then (A) b has a jump at c (B) b has a jump at a (C) b is strictly increasing over (a,c) (D) b is constant over (a,c)

Also written as: Let F:R->R be a distribution function and define b(c)=inf F^(-1)([c,1]) for c in (0,1] (and b(0)=0). If F has a jump at x, say c=F(x)>a>= F(x-), then

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.

Practise Random variables and standard distributionsMore on Random variables, PMFs, PDFs and CDFs

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Question from the DSE 2015 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.