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 192376 by Spillover last updated on 16/May/23 $${Find}\:{the}\:{first}\:{four}\:{moment}\:{of}\:{the} \\ $$$${binomial}\:{distribution} \\ $$$$ \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 61303 by mr W last updated on 31/May/19 Commented by mr W last updated on 31/May/19 $${A}\:{small}\:{sphere}\:\left({say}\:{the}\:{moon}\right)\:{moves} \\ $$$${around}\:{a}\:{big}\:{sphere}\:\left({say}\:{the}\:{earth}\right)\:{in} \\ $$$${a}\:{circular}\:{track}.\:{A}\:{point}\:{source}\:\left({say}\right. \\ $$$$\left.{the}\:{sun}\right)\:{is}\:{at}\:{a}\:{distance}\:{e}\:{from}\:{the}…
Question Number 192375 by Spillover last updated on 16/May/23 $${Show}\:{that}\:{E}\left({Z}\right)=\mathrm{0}\:\:\:{and}\:{Var}\left({Z}\right)=\mathrm{1}\:{where} \\ $$$${Z}\:{is}\:{the}\:{standard}\:{normal}\:{variable} \\ $$ Answered by mehdee42 last updated on 16/May/23 $${We}\:{know}\:\because\:\:\:{Z}=\frac{{x}−\mu}{\sigma}\:\:\: \\ $$$$\&\:\:{E}\left({kx}\right)={kE}\left({x}\right)\:\:\&\:\:{E}\left({x}+{k}\right)={E}\left({x}\right)+{k}\:\:;\:{k}\in\mathbb{R} \\…
Question Number 126836 by mohammad17 last updated on 24/Dec/20 Commented by mohammad17 last updated on 24/Dec/20 $${help}\:{me}\:{sir} \\ $$ Commented by mohammad17 last updated on…
Question Number 192374 by mehdee42 last updated on 15/May/23 $${why}\:\:\:“\:\mathrm{200}!<\mathrm{100}^{\mathrm{200}} \:''\:? \\ $$ Commented by mehdee42 last updated on 17/May/23 $$\mathrm{99}×\mathrm{101}<\mathrm{100}^{\mathrm{2}} \\ $$$$\mathrm{98}×\mathrm{102}<\mathrm{100}^{\mathrm{2}} \\ $$$$:…
Question Number 126837 by mohammad17 last updated on 24/Dec/20 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 126835 by mohammad17 last updated on 24/Dec/20 Answered by liberty last updated on 25/Dec/20 $$\:\begin{pmatrix}{{x}}\\{{y}}\end{pmatrix}\:=\:\begin{pmatrix}{\mathrm{cos}\:\frac{\pi}{\mathrm{6}}\:\:\:\:\:\:\:−\mathrm{sin}\:\frac{\pi}{\mathrm{6}}}\\{\mathrm{sin}\:\frac{\pi}{\mathrm{6}}\:\:\:\:\:\:\:\:\:\:\:\mathrm{cos}\:\frac{\pi}{\mathrm{6}}}\end{pmatrix}^{−\mathrm{1}} \begin{pmatrix}{{x}'}\\{{y}'}\end{pmatrix}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:=\:\begin{pmatrix}{\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}\:\:\:\:\:\:\:−\frac{\mathrm{1}}{\mathrm{2}}}\\{\frac{\mathrm{1}}{\mathrm{2}}\:\:\:\:\:\:\:\:\:\:\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}}\end{pmatrix}^{−\mathrm{1}} \begin{pmatrix}{{x}'}\\{{y}'}\end{pmatrix} \\ $$$$\:\:\:\:\:\:\:\:\:=\:\mathrm{1}\begin{pmatrix}{\:\:\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\frac{\mathrm{1}}{\mathrm{2}}}\\{−\frac{\mathrm{1}}{\mathrm{2}}\:\:\:\:\:\:\:\:\:\:\:\:\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}}\end{pmatrix}\:\begin{pmatrix}{{x}'}\\{{y}'}\end{pmatrix} \\ $$$$\:\:\:\:\:\:\:\:\:=\:\begin{pmatrix}{\frac{\mathrm{1}}{\mathrm{2}}\left(\sqrt{\mathrm{3}}\:{x}'+{y}'\right)}\\{\frac{\mathrm{1}}{\mathrm{2}}\left(−{x}'+\sqrt{\mathrm{3}}\:{y}'\right.}\end{pmatrix}…
Question Number 61297 by alphaprime last updated on 31/May/19 $$\mathrm{A}\:\mathrm{container}\:\mathrm{is}\:\mathrm{50\%}\:\mathrm{full}\:\mathrm{of}\:\mathrm{water}\:\mathrm{at}\:\mathrm{triple}\:\mathrm{point} \\ $$$$\mathrm{phase}\:.\:\mathrm{It}'\mathrm{s}\:\mathrm{Isolated}\:\mathrm{and}\:\mathrm{subjected}\:\mathrm{to}\:\mathrm{space} \\ $$$$\mathrm{system}\:\mathrm{defining}\:\mathrm{no}\:\mathrm{gravity}\:\mathrm{acting}\:\mathrm{on}\:\mathrm{the}\: \\ $$$$\mathrm{particles}\:,\:\mathrm{Which}\:\mathrm{state}\:\mathrm{of}\:\mathrm{matter}\:\mathrm{is}\:\mathrm{now} \\ $$$$\mathrm{more}\:\mathrm{dominant}\:,\:\mathrm{solid}\:,\:\mathrm{liquid}\:,\:\mathrm{or}\:\mathrm{gas}\:? \\ $$$$\mathrm{Calculate}\:\mathrm{the}\:\mathrm{intermolecular}\:\mathrm{distances} \\ $$$$\mathrm{between}\:\mathrm{simultaneous}\:\mathrm{two}\:\mathrm{distinct}\:\mathrm{states} \\ $$$$\mathrm{of}\:\mathrm{water}.\: \\…
Question Number 192370 by Tawa11 last updated on 15/May/23 $$\mathrm{Solve}\:\mathrm{the}\:\mathrm{equation}\:\:\:\mathrm{x}^{\mathrm{4}} \:\:−\:\:\mathrm{2x}^{\mathrm{3}} \:\:+\:\:\mathrm{4x}^{\mathrm{2}} \:\:+\:\:\mathrm{6x}\:\:\:−\:\:\mathrm{21}\:\:\:=\:\:\:\mathrm{0},\:\: \\ $$$$\mathrm{Given}\:\mathrm{that}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{two}\:\mathrm{of}\:\mathrm{its}\:\mathrm{roots}\:\mathrm{is}\:\mathrm{zero} \\ $$ Answered by Frix last updated on 16/May/23 $$\left({x}−{a}\right)\left({x}+{a}\right)\left({x}−{b}\right)\left({x}−{c}\right)=\mathrm{0}…