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Questions › DSE › DSE 2010 › Q48
2 marksStatistics › Random variables and standard distributions › Random variables, PMFs, PDFs and CDFsModerateabout 3 min

DSE 2010 Question 48: Random variables and standard distributions

The number of loaves of bread sold by a bakery in a day is a random variable XXX with density f(x)=kxf(x)=kxf(x)=kx for x∈[0,5)x\in[0,5)x∈[0,5), f(x)=k(10−x)f(x)=k(10-x)f(x)=k(10−x) for x∈[5,10)x\in[5,10)x∈[5,10), and 000 for x≥10x\ge 10x≥10. As fff is a probability density function, the value of kkk must be

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The number of loaves of bread sold by a bakery in a day is a random variable X with density f(x)=kx for x∈[0,5), f(x)=k(10-x) for x∈[5,10), and 0 for x≥ 10. As f is a probability density function, the value of k must be (A) 0 (B) -2/25 (C) 1/25 (D) 2/75

Also written as: The number of loaves of bread sold by a bakery in a day is a random variable X with density f(x)=kx for x in [0,5), f(x)=k(10-x) for x in [5,10), and 0 for x>= 10. As f is a probability density function, the value of k must be

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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Question from the DSE 2010 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.