Science:Math Exam Resources/Courses/MATH103/April 2017/Question 01 (e) (ii)

MATH103 April 2017

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Question 01 (e) (ii)
Plots (A-D) depict probability density functions, pdf ’s, for $-\infty <x<\infty$ at the same scale. List all pdf ’s that satisfy the following criteria: (${\bar {x}}$ denotes the mean and $x_{med}$ the median) (ii) $x_{med}>{\bar {x}}$?

Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you?

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Hint
Review the hint for last question.

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Solution

Found a typo? Is this solution unclear? Let us know here. Please rate my easiness! It's quick and helps everyone guide their studies. Like what has been explained in last question, the answer will be B. The mean will on the left side of median: the point that separates the area into two equal parts will on the left side of y-axis, while the mean will be even further left because it is the integral of terms of the form $xp(x)\Delta x$. It is not only dragged by $p(x)\Delta x$ like the median, but also by $x$. In other words, the ``tail" of the distribution is larger on the left side than on the right side. answer: $\color {blue}B$