The continuous random variable $X$ has probability density function $\mathrm{f}(x) = kx^2$, wher

Question

The continuous random variable $X$ has probability density function $\mathrm{f}(x) = kx^2$, where $0 \le x \le 2$. Find the value of the constant $k$. Sketch the graph of $y = \mathrm{f}(x)$. Find $\mathrm{P}(X \ge 1)$. Find $\mathrm{P}(0.5 \le X < 1.5)$.

Accepted Answer

(i) $ \frac{3}{8}$; (iii) $ 0.875$; (iv) $0.406$.

Finding the value of an unknown in CRV

Finding the value of an unknown in CRV