If $X$ is a continuous random variable with probability density function \(\mathrm{f}(x) = \f

Question

If $X$ is a continuous random variable with probability density function $\mathrm{f}(x) = \frac{1}{8}x$, where $0 \leq x \leq 4$. Find the cumulative distribution function $F(x)$ and sketch $y = F(x)$. Find the median $m$, the upper quartile $s$ and the lower quartile $r$. Find $\mathrm{P}(0.3 < X \leq 1.8)$

Accepted Answer

(a) $F(x) = \frac{x^2}{16}, 0 \leq x \leq 4$; (b) $\sqrt{8}, \sqrt{12}, 2$ (c) $0.197$.

Calculating median and IQR of a CRV

Calculating median and IQR of a CRV