Paper 7 October/November 2010 MATHEMATICS (9709/73) A Levels
لطفا برای اطمینان از عملکرد و تجربه بهتر از مرورگرهای مدرن و به روز مانند کروم یا فایرفاکس استفاده کنید.

A random variable $X$ has probability density function given by
$f\left( x \right) = \left\{ \begin{gathered} k\left( {1 - x} \right)\,\,\,\,\,\,\,\,\,\,\,\,\,\, - 1 \leqslant x \leqslant 1, \hfill \\ 0\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,otherwise, \hfill \\ \end{gathered} \right.$
where $k$ is a constant.
a) Show that $k = \frac{1}{2}$.
b) Find $P\left( {X \gt \frac{1}{2}} \right)$