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

Question

The continuous random variable $X$ has probability density function given by $$\mathrm{f}(x) = \begin{cases} k & , \quad 0 \leq x < 2 \ k(2x - 3) & , \quad 2 \leq x \leq 3 \ 0 & , \quad \text{otherwise} \end{cases}$$ Find the value of the constant $k$. Sketch the graph of $y = \mathrm{f}(x)$. Find $\mathrm{P}(X \leq 1)$. Find $\mathrm{P}(X > 2.5)$. Find $\mathrm{P}(1 \leq X \leq 2.3)$.

Accepted Answer

(a) $k = \frac{1}{4}$; (b)$\frac{1}{4}$; (c)$0.3125 = \frac{5}{16}$; (d)$0.3475 = \frac{139}{400}$.

Finding the value of an unknown in a CRV

Finding the value of an unknown in a CRV