The continuous random variable \(X\) is such that
\[P(X &gt; x) = \begin{cases} 1 & , & x \le 0 \\ k(3 - x)^3 & , & 0 &lt; x &lt; 3 \\ 0 & , & x \ge 3 \end{cases}\]
Show that&nbsp;\(\mathrm{P}(X &gt; 1) = \frac{8}{27}\).
Find the probability density function of \(X\), and hence find \(\mathrm{E}(X)\).

The continuous random variable \(X\) is such that

\[P(X > x) = \begin{cases} 1 & , & x \le 0 \\ k(3 - x)^3 & , & 0 < x < 3 \\ 0 & , & x \ge 3 \end{cases}\]

Show that \(\mathrm{P}(X > 1) = \frac{8}{27}\).

Find the probability density function of \(X\), and hence find \(\mathrm{E}(X)\).

Probability - General

Probability

International Baccalaureate Higher Level Mathematics

Calculating pdf from a given cdf

Calculating pdf from a given cdf