Mathematics Statistics 2 9709: Continuous Random Variables Topical Past Paper Questions

A random variable X has probability density function given by $$ \mathrm{f}(x)=\left\{\begin{aligned}&k(3x-x^{2})\quad&0\leq x\leq3,\\ &0\quad&otherwise.\end{aligned}\right. $$ (i) Show that $ k = \frac{2}{9} $. [3] (ii) Find P(1 ≤ X ≤ 2). [2] ……

The random variable X has probability density function given by $$ \mathrm{f}(\boldsymbol{x})=\left\{\begin{aligned}{}&{{}k x^{-1}}&{\quad2\leqslant x\leqslant6,}\\ {}&{{}0}&{\quad\mathrm{o t h e r w i s e},}\\ \end{aligned}\right. $$ where $k$ is a constant. (i) Show that $ k =…

A continuous random variable, X, has probability density function given by $$ \mathrm{f}(x)=\left\{\begin{aligned}&\tfrac{1}{4}(x+1)&\quad&0\leq x\leq2,\\ &0&\quad&otherwise.\end{aligned}\right. $$ (i) Find E(X). [3] (ii) Find the median of X. [3]