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Questions › JNU › JNU SIS 2018 › Q20
2 marks, −1Statistics › Random variables and standard distributions › Random variables, PMFs, PDFs and CDFsModerateabout 2 min

JNU SIS 2018 Question 20: Random variables and standard distributions

Suppose that XXX is a random variable with the following distribution function :

F(x)={0; for x<0x8; for 0≤x<12+x8; for 1≤x<29+x12; for 2≤x<31; for x≥3F(x) = \begin{cases} 0 & ; \text{ for } x < 0 \\ \dfrac{x}{8} & ; \text{ for } 0 \le x < 1 \\ \dfrac{2 + x}{8} & ; \text{ for } 1 \le x < 2 \\ \dfrac{9 + x}{12} & ; \text{ for } 2 \le x < 3 \\ 1 & ; \text{ for } x \ge 3 \end{cases}F(x)=⎩⎨⎧​08x​82+x​129+x​1​; for x<0; for 0≤x<1; for 1≤x<2; for 2≤x<3; for x≥3​

Then P(1≤X≤2)P(1 \le X \le 2)P(1≤X≤2) is

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Suppose that X is a random variable with the following distribution function: F(x) = { 0; for x < 0; x/8; for 0 ≤ x < 1; (2 + x)/8; for 1 ≤ x < 2; (9 + x)/12; for 2 ≤ x < 3; 1; for x ≥ 3 } Then P(1 ≤ X ≤ 2) is (A) 1/8 (B) 3/8 (C) 19/24 (D) 13/24

Also written as: Suppose that X is a random variable with the following distribution function: F(x) = { 0; for x < 0; x/8; for 0 <= x < 1; (2 + x)/8; for 1 <= x < 2; (9 + x)/12; for 2 <= x < 3; 1; for x >= 3 } Then P(1 <= X <= 2) is

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 JNU SIS 2018 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.