Further Mathematics 9231: Continuous random variable Topical Past Paper Questions

The diagram shows the continuous random variable X with probability density function f given by $$ \mathrm{f}(x)=\left\{\begin{aligned}&a(x-1)&\quad1\leqslant x\leqslant5,\\ &b(x-7)^{2}&\quad5\leqslant x\leqslant7,\\ &0&\quad\text{otherwise}.\end{aligned}\right. $$ The upper quar…

The continuous random variable X has probability density function f given by $$ \mathrm{f}(x)=\left\{\begin{aligned}&\frac{4}{9}(x+1)&\quad&0\leqslant x\leqslant1,\\ &(x-2)^{2}&\quad&1 [2] The random variable Y is defined by $ Y = \sqrt{X} $. (c) Find the cumulative distribution…

The continuous random variable X has probability density function f given by $$ \mathrm{f}(x)=\left\{\begin{aligned}&kx^{3}&\quad&0\leqslant x<1,\\ &k(5-x)&\quad&1\leqslant x\leqslant5,\\ &0&\quad&otherwise,\end{aligned}\right. $$ where k is a constant. (a) Sketch the graph of f.…