Category: Probability and Statistics

Question Number 128103 by byaw last updated on 04/Jan/21 $$ \\ $$$$\mathrm{A}\:\mathrm{box}\:\mathrm{contains}\:\mathrm{4}\:\mathrm{black}\:\mathrm{5}\:\mathrm{white} \\ $$$$\mathrm{and}\:\mathrm{6}\:\mathrm{red}\:\mathrm{shirts}.\:\mathrm{3}\:\mathrm{are}\:\mathrm{drawn}\:\mathrm{from} \\ $$$$\mathrm{the}\:\mathrm{box}\:\mathrm{one}\:\mathrm{after}\:\mathrm{the}\:\mathrm{other}\: \\ $$$$\mathrm{without}\:\mathrm{replacement}.\:\mathrm{Find}\:\mathrm{the} \\ $$$$\mathrm{proability}\:\mathrm{that}\:\mathrm{two}\:\mathrm{of}\:\mathrm{the}\:\mathrm{same} \\ $$$$\mathrm{color}\:\mathrm{and}\:\mathrm{one}\:\mathrm{a}\:\mathrm{different}\:\mathrm{color}. \\ $$ Answered…

Question Number 192622 by sg74656 last updated on 23/May/23 $$\frac{\mathrm{3}}{\mathrm{2}}\mathrm{cos}^{−\mathrm{1}} \sqrt{\frac{\mathrm{2}}{\mathrm{2}+\pi^{\mathrm{2}} }}+\frac{\mathrm{1}}{\mathrm{4}}\mathrm{sin}^{−\mathrm{1}} \frac{\mathrm{2}\sqrt{\mathrm{2}\pi}}{\mathrm{2}+\pi^{\mathrm{2}} }+\mathrm{tan}^{−\mathrm{1}} \frac{\sqrt{\mathrm{2}}}{\pi} \\ $$ Answered by witcher3 last updated on 24/May/23 $$\mathrm{nice}\:\mathrm{one}\:\mathrm{tchek}\:\mathrm{please}\:\mathrm{the}\:\mathrm{expression}\:\mathrm{if}\:\mathrm{it}\:\mathrm{is}\:\mathrm{correct}…

Question Number 192377 by Spillover last updated on 16/May/23 $${The}\:{probability}\:{density}\:{function}\:{f}\left({x}\right) \\ $$$$\:{of}\:{a}\:{variable}\:{x}\:{is}\:{given}\:{by}\: \\ $$$${f}\left({x}\right)=\begin{cases}{{kx}\mathrm{sin}\:\pi{x}\:\:\:\:\:\mathrm{0}\leqslant{x}\leqslant\mathrm{1}}\\{\mathrm{0}\:{for}\:{all}\:{value}\:{of}\:{x}}\end{cases} \\ $$$${Show}\:{that}\:{k}=\pi\:\:{and}\:{deduce}\:{that}\:{mean}\: \\ $$$${and}\:{the}\:{variance}\:{of}\:{the}\:{distribution}\:{are} \\ $$$$\left(\mathrm{1}−\frac{\mathrm{4}}{\pi^{\mathrm{2}} }\right)\:{and}\:\frac{\mathrm{2}}{\pi^{\mathrm{2}} }\left(\mathrm{1}−\frac{\mathrm{8}}{\pi^{\mathrm{2}} }\right) \\ $$…

Question Number 192255 by Spillover last updated on 01/Feb/24 $${If}\:\theta\:{be}\:{the}\:{acute}\:{angle}\:{between}\:{two}\:{regression} \\ $$$${line}\:{in}\:{the}\:{case}\:{of}\:{two}\:{variables}\:{x}\:{and}\:{y} \\ $$$${Show}\:{that} \\ $$$$\:\:\mathrm{tan}\:\theta=\frac{\mathrm{1}−{r}}{{r}}.\frac{\sigma_{{x}} \sigma_{{y}} }{\sigma_{{x}} ^{\mathrm{2}} +\sigma_{{y}} ^{\mathrm{2}} }\:\:\: \\ $$$${where}\:\:{r},\sigma_{{x}} ,\sigma_{{y}}…

Question Number 192118 by Red1ight last updated on 08/May/23 $$\mathrm{given}\:\mathrm{points}\:\left({a},{b}\right)\:\mathrm{where}\:{a},{b}\:\in\mathbb{R} \\ $$$$\mathrm{how}\:\mathrm{to}\:\mathrm{get}\:\mathrm{the}\:\mathrm{best}\:\mathrm{fit}\:\mathrm{parabola}\:\mathrm{that}\:\mathrm{go}\:\mathrm{through}\:\mathrm{the}\:\mathrm{origin} \\ $$$$\mathrm{and}\:\mathrm{open}\:\mathrm{downward}\:\left(\mathrm{coefficient}\:\mathrm{of}\:{x}^{\mathrm{2}} \:\mathrm{is}\:\mathrm{negative}\right)? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com