The continuous random variable $X$ has probability density function given by $\mathrm{f}(x)$ whe

Question

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 $P(|X| < 0.5$.

Accepted Answer

(a) $0$; (b) $0.688$.

Finding the mode of a CRV

Finding the mode of a CRV