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Question Number 181677 by ali009 last updated on 28/Nov/22
$$\:{the}\:{distirbution}\:{function}\:{for}\:{a}\:{random} \\ $$ $${variable}\:{X}\:{is} \\ $$ $${F}\left({x}\right)=\begin{cases}{\mathrm{1}−\mathrm{2}{e}^{−\mathrm{2}{x}} \:\:\:\:\:\:\:\:\:\:\:\:\:\:{x}\geqslant\mathrm{0}}\\{\mathrm{0}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{x}<\mathrm{0}}\end{cases} \\ $$ $${find} \\ $$ $$\left.\mathrm{1}\right){the}\:{density}\:{function}\:{f}\left({x}\right) \\ $$ $$\left.\mathrm{2}\right){p}\left({x}>\mathrm{2}\right) \\ $$ $$\left.\mathrm{3}\right){p}\left(−\mathrm{3}<{x}\leqslant\mathrm{4}\right) \\ $$