A continuous random variable $$\(X\)$$ has probability density function $$\[ \mathrm{f}(x)=\left\{\begin{array}{cc} k(a-x)^{2} & 0 \leqslant x \leqslant a \\ 0 & \text { otherwise } \end{array}\right. \]$$ where $$\(k\)$$ and $$\(a\)$$ are constants. (a) Show that $$\(k a^{3}=3\)$$ (3) Given that $$\(\mathrm{E}(X)=1.5\)$$ (b) use algebraic integration to show that $$\(a=6\)$$ (4) (c) Verify that the median of $$\(X\)$$ is 1.2 to one decimal place. (3)

Answer:

Knowledge points:

Solution: