Finding the mode of a CRV
Finding the mode of a CRV
IB Year 5 | Grade 11
The continuous random variable \(X\) has probability density function given by \(\mathrm{f}(x)\) where
\[ \mathrm{f}(x) = \begin{cases} \frac{3}{4}(1-x^2), & -1 \leq x \leq 1 \\ 0, & \text{otherwise} \end{cases} \]
- Sketch \(y = \mathrm{f}(x)\) and hence find the mode of \(X\).
- Find \(P(|X| < 0.5)\).
Solution:
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Answer:(a) see sketch; mode \(0\). (b) \(11/16\).
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