Question Number 180734 by srikanth2684 last updated on 16/Nov/22
$${If}\:{f}\left({x}\right)=\left\{_{\mathrm{0},\:{othrrwise}} ^{\mathrm{2}{x}\:,\:\mathrm{0}\leqslant{x}\leqslant{a}} \:{is}\:{a}\:{probability}\right. \\ $$$${density}\:{funtion}\:{of}\:{a}\:{random}\: \\ $$$${variable},\:{then}\:{a}=? \\ $$$${pls}\:{solve} \\ $$
Answered by cortano1 last updated on 16/Nov/22
$$\:\underset{\mathrm{0}} {\overset{{a}} {\int}}\:{f}\left({x}\right){dx}\:=\:\mathrm{1}\Rightarrow\underset{\mathrm{0}} {\overset{{a}} {\int}}\mathrm{2}{x}\:{dx}=\mathrm{1} \\ $$$$\Rightarrow{a}^{\mathrm{2}} \:=\:\mathrm{1};\:{a}=\mathrm{1}\:\left(\:\mathrm{since}\:{a}>\mathrm{0}\:\right) \\ $$
Commented by srikanth2684 last updated on 16/Nov/22
$${thank}\:{you} \\ $$