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 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 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 $${We}\:{know}\:\because\:\:\:{Z}=\frac{{x}−\mu}{\sigma}\:\:\: \\ $$$$\&\:\:{E}\left({kx}\right)={kE}\left({x}\right)\:\:\&\:\:{E}\left({x}+{k}\right)={E}\left({x}\right)+{k}\:\:;\:{k}\in\mathbb{R} \\…
Question Number 192255 by Spillover last updated on 01/Feb/24 $${If}\:\theta\:{be}\:{the}\:{acute}\:{angle}\:{between}\:{two}\:{regression} \\ $$$${line}\:{in}\:{the}\:{case}\:{of}\:{two}\:{variables}\:{x}\:{and}\:{y} \\ $$$${Show}\:{that} \\ $$$$\:\:\mathrm{tan}\:\theta=\frac{\mathrm{1}−{r}}{{r}}.\frac{\sigma_{{x}} \sigma_{{y}} }{\sigma_{{x}} ^{\mathrm{2}} +\sigma_{{y}} ^{\mathrm{2}} }\:\:\: \\ $$$${where}\:\:{r},\sigma_{{x}} ,\sigma_{{y}}…
Question Number 192254 by Spillover last updated on 01/Feb/24 $${Establish}\:{the}\:{formular}\:\: \\ $$$$\sigma_{{x}−{y}} ^{\mathrm{2}} =\sigma_{{x}} ^{\mathrm{2}} +\sigma_{{y}} ^{\mathrm{2}} −\mathrm{2}{r}\sigma_{{x}} \sigma_{{y}} \:\: \\ $$$${where}\:{by}\:{r}\:{is}\:{the}\:{correlation} \\ $$$${coefficient}\:{between}\:{x}\:{and}\:{y} \\…
Question Number 192118 by Red1ight last updated on 08/May/23 $$\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
Question Number 192112 by Spillover last updated on 08/May/23 $${prove}\:{that}.\:\:\:\:\:\:\:\mathrm{0}!=\mathrm{1} \\ $$ Commented by Frix last updated on 08/May/23 $$\mathrm{I}\:\mathrm{think}\:\mathrm{it}'\mathrm{s}\:\mathrm{defined}\:\mathrm{0}!=\mathrm{1}\: \\ $$$$\mathrm{There}'\mathrm{s}\:\mathrm{the}\:\mathrm{idea}\:\mathrm{of}\:\mathrm{the}\:“\mathrm{Empty}\:\mathrm{Product}'' \\ $$$$\:\:\:\:\:\mathrm{It}'\mathrm{s}\:\mathrm{obvious}\:\mathrm{that}\:\mathrm{the}\:“\mathrm{Empty}\:\mathrm{Sum}''=\mathrm{0} \\…
Question Number 192104 by Spillover last updated on 08/May/23 Answered by otchereabdullai@gmail.com last updated on 08/May/23 $${a}.\:\frac{\mathrm{12}!}{\mathrm{2}!\mathrm{2}!\mathrm{2}!}\:=\mathrm{59875200}\:{ways} \\ $$$${b}.\:\:\frac{\mathrm{11}!}{\mathrm{2}!\mathrm{2}!}\:=\:\mathrm{9979200}\:{ways} \\ $$ Commented by Spillover last…
Question Number 192105 by Spillover last updated on 08/May/23 Answered by mehdee42 last updated on 09/May/23 $$\left.\:{a}\right)\:\:\:{lema}\::\:{if}\:\:\mathrm{0}<{x}<\mathrm{1}\:\Rightarrow\:\underset{{i}=\mathrm{0}} {\overset{\infty} {\sum}}{ix}^{{i}} =\frac{{x}}{\left(\mathrm{1}−{x}\right)^{\mathrm{2}} }\:\:\:\&\:\:\:\underset{{i}=\mathrm{0}} {\overset{\infty} {\sum}}{i}^{\mathrm{2}} {x}^{{i}} =\frac{{x}\left(\mathrm{1}+{x}\right)}{\left(\mathrm{1}−{x}\right)^{\mathrm{3}}…
Question Number 192103 by Spillover last updated on 08/May/23 Answered by otchereabdullai@gmail.com last updated on 08/May/23 $${the}\:{most}\:{important}\:{thing}\:{to}\:{know}\:{is} \\ $$$${we}\:{cant}\:{start}\:{the}\:{number}\:{with}\:{zero} \\ $$$${since}\:{is}\:{a}\:{four}\:{digit}\:{mumber}\:{without} \\ $$$${repetition} \\ $$$${the}\:{first}\:{can}\:{be}\:{chosen}\:{in}\:\mathrm{5}\:{ways},…