Let $X$ be a continuous rv with cdf
\[
F(x)=\begin{cases}
       0, & x\leqslant 0, \\
       \frac{x}{4}\Bigl[1+\ln(\frac{4}{x})\Bigr], & 0 < x\leqslant 4, \\
       1, & x > 4.
     \end{cases}
\]
[This type of cdf is suggested in the article "Variability in Measured Bedload-Transport Rates" (Water Resources Bull., 1985:39--48) as a model for a certain hydrologic variable.] What is

• (a) $P(X\leqslant 1)$?
• (b) $P(1\leqslant X\leqslant 3)$?
• (c) The pdf of $X$?