Question Number 80746 by jagoll last updated on 06/Feb/20 $${what}\:{is}\:{constan}\:{term}\:{in}\:{expansion} \\ $$$$\left(\mathrm{1}+\mathrm{3}{x}\right)^{\mathrm{5}} \left(\frac{\mathrm{3}}{{x}}+\mathrm{1}\right)^{\mathrm{2}} \\ $$ Commented by jagoll last updated on 06/Feb/20 $${c}\left({x}\right)\:=\:\frac{\left(\mathrm{1}+\mathrm{3}{x}\right)^{\mathrm{5}} \left(\mathrm{3}+{x}\right)^{\mathrm{2}} }{{x}^{\mathrm{2}}…
Question Number 145869 by Ar Brandon last updated on 09/Jul/21 $$\mathrm{Let}\:\mathrm{A}\:\mathrm{and}\:\mathrm{B}\:\mathrm{be}\:\mathrm{2}\:\mathrm{events}\:\mathrm{such}\:\mathrm{that}\:\mathrm{P}\left(\mathrm{A}\right)=\mathrm{0}.\mathrm{4},\:\mathrm{P}\left(\overset{−} {\mathrm{B}}/\mathrm{A}\right)=\mathrm{0}.\mathrm{7} \\ $$$$\:\mathrm{and}\:\mathrm{P}\left(\mathrm{B}/\overset{−} {\mathrm{A}}\right)=\mathrm{0}.\mathrm{6},\:\mathrm{then}\:\mathrm{find} \\ $$$$\left({i}\right)\mathrm{P}\left(\overset{−} {\mathrm{B}}/\overset{−} {\mathrm{A}}\right)\:\:\left({ii}\right)\mathrm{P}\left(\mathrm{A}\cap\mathrm{B}\right)\:\:\:\left({iii}\right)\:\mathrm{P}\left(\mathrm{B}\right)\:\:\left({iv}\right)\mathrm{P}\left(\mathrm{A}\cup\mathrm{B}\right) \\ $$ Answered by gsk2684 last…
Question Number 145831 by nadovic last updated on 08/Jul/21 $$\:\mathrm{A}\:\mathrm{box}\:\boldsymbol{{P}},\:\mathrm{contains}\:\mathrm{4}\:\mathrm{white},\:\mathrm{2}\:\mathrm{green}\:\mathrm{and}\: \\ $$$$\:\mathrm{3}\:\mathrm{blue}\:\mathrm{cards}.\:\mathrm{Another}\:\mathrm{box}\:\boldsymbol{{Q}},\:\mathrm{contains} \\ $$$$\:\mathrm{2}\:\mathrm{white},\:\mathrm{3}\:\mathrm{green}\:\mathrm{and}\:\mathrm{2}\:\mathrm{blue}\:\mathrm{cards}.\:\mathrm{A}\:\mathrm{card} \\ $$$$\:\mathrm{is}\:\mathrm{picked}\:\mathrm{at}\:\mathrm{random}\:\mathrm{from}\:\boldsymbol{{P}}\:\mathrm{and}\:\mathrm{placed} \\ $$$$\:\mathrm{in}\:\boldsymbol{{Q}}.\:\mathrm{A}\:\mathrm{card}\:\mathrm{is}\:\mathrm{then}\:\mathrm{picked}\:\mathrm{from}\:\boldsymbol{{Q}}. \\ $$$$\:\mathrm{Find}\:\mathrm{the}\:\mathrm{probability}\:\mathrm{that}\:\mathrm{the} \\ $$$$\:\:\left({a}\right)\:\:\mathrm{card}\:\mathrm{picked}\:\mathrm{from}\:\boldsymbol{{Q}}\:\mathrm{is}\:\mathrm{white}. \\ $$$$\:\:\left({b}\right)\:\:\mathrm{cards}\:\mathrm{picked}\:\mathrm{from}\:\boldsymbol{{P}}\:\mathrm{and}\:\boldsymbol{{Q}}\:\mathrm{are}\:\mathrm{of} \\…
Question Number 145678 by syamilkamil1 last updated on 07/Jul/21 $${let}\:{X}_{\mathrm{1}} \:{and}\:{X}_{\mathrm{2}\:} \:{be}\:{independent}\:{random}\:{variable}\: \\ $$$${of}\:{uniform}\:{distribution}\:.\:{If}\:{it}\:{is}\:{known}\:{that} \\ $$$${X}_{{i}} \sim{uniform}\:\left(\mathrm{0},\mathrm{1}\right)\:{and}\:{let}\:{S}\:=\:{X}_{\mathrm{1}} \:+\:{X}_{\mathrm{2}} \\ $$$${Determine}\:{the}\:{Probability}\:{density}\:{function} \\ $$$${from}\:{S}! \\ $$ Terms…
Question Number 145674 by syamilkamil1 last updated on 07/Jul/21 $${the}\:{probability}\:{density}\:{function}\:{with}\:{two}\:{continous}\:{random} \\ $$$${variable}\:{X}\:{and}\:{Y}\:{is}\:{a}\:{follows}\:: \\ $$$$ \\ $$$${f}\left({x},{y}\right)\:=\:\left\{_{\mathrm{0}\:\:,\:{x}\:{other}} ^{\mathrm{2}{x}\:+\:\mathrm{2}{y}\:\:,\:\mathrm{0}\:<\:{x}\:<\:\mathrm{1},\:\mathrm{0}\:<\:{y}\:<\:\mathrm{1}} \right. \\ $$$$ \\ $$$${determine}\:{the}\:{correlation}\:{coefficient} \\ $$$${between}\:{X}\:{and}\:{Y}! \\…
Question Number 145675 by syamilkamil1 last updated on 07/Jul/21 $${the}\:{probabilty}\:{density}\:{function} \\ $$$${is}\:{known}\:{as}\:{follows}\:: \\ $$$${f}\left({x}\right)\:=\:\left\{_{\mathrm{0}\:\:\:,\:{x}\:{other}} ^{{cx}^{\mathrm{3}} \:\:\:,\:\mathrm{0}\:<\:{x}\:<\:\mathrm{4}} \right. \\ $$$${define}\:{P}\left(\mathrm{1}\:<\:{x}\:<\:\mathrm{2}\right)! \\ $$$$ \\ $$$$ \\ $$$$…
Question Number 145583 by ArielVyny last updated on 06/Jul/21 $${une}\:{urne}\:{contient}\:{N}\:{boules}\:{dont} \\ $$$${M}\:{boules}\:{blanches}\:{et}\:{N}−{M}\:{boule}\:{noires} \\ $$$${on}\:{tire}\:{successivement}\:{et}\:{sans}\:{remise} \\ $$$${n}\:{boules}\:{de}\:{l}'{urne}. \\ $$$${soit}\:{A}_{{i}} :''{prelever}\:{une}\:{boules}\:{noires}\:{au}\:{ieme} \\ $$$${tirage}'' \\ $$$${calculer}\:{P}\left({A}_{{i}} \right) \\…
Question Number 145557 by puissant last updated on 06/Jul/21 Answered by Olaf_Thorendsen last updated on 06/Jul/21 $$\left.\mathrm{1}\right) \\ $$$$\mathrm{R}_{{n}} \left({x}\right)\:=\:\left(\mathrm{1}+{x}\right)^{{n}} \:=\:\underset{{k}=\mathrm{0}} {\overset{{n}} {\sum}}\mathrm{C}_{{n}} ^{{k}} {x}^{{k}}…
Question Number 145553 by puissant last updated on 05/Jul/21 Answered by Olaf_Thorendsen last updated on 06/Jul/21 $${On}\:{a}\:{vu}\:{dans}\:{une}\:{question}\: \\ $$$${precedente}\:{que}\:\left(\mathrm{Q}.\mathrm{145557}\right)\:: \\ $$$$\mathrm{C}_{{p}+{q}} ^{{n}} \:=\:\underset{{k}=\mathrm{0}} {\overset{{n}} {\sum}}\mathrm{C}_{{p}}…
Question Number 145468 by puissant last updated on 05/Jul/21 Answered by Olaf_Thorendsen last updated on 05/Jul/21 $$\left.{a}\right) \\ $$$$\mathrm{On}\:\mathrm{note}\:\mathrm{X}\:\mathrm{la}\:\mathrm{variable}\:\mathrm{qui}\:\mathrm{comptabilise} \\ $$$$\mathrm{le}\:\mathrm{nombre}\:\mathrm{de}\:\mathrm{bonnes}\:\mathrm{pieces}\:\mathrm{dans}\:\mathrm{le} \\ $$$$\mathrm{tirage}\:: \\ $$$${p}\left(\mathrm{X}=\mathrm{4}\right)\:=\:\frac{\mathrm{C}_{\mathrm{16}}…