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Statistics, 2ADV 2026 HSC 2 MC

A probability density function is shown in the diagram.
 

What is the mode of the given probability density function?

  1. \(0\)
  2. \(\dfrac{\sqrt{2}}{2}\)
  3. \(2\)
  4. \(2\sqrt{2}\)
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\(D\)

Show Worked Solution

\(\text{Mode occurs when}\ f(x)\ \text{is a maximum.}\)

\(f(x)_{\text{max}}\ \text{occurs at}\ \ x=2\sqrt{2}\ \ \text{(closed circle)}\)

\(\Rightarrow D\)