Question Number 132086 by SLVR last updated on 11/Feb/21 $$ \\ $$ Commented by mr W last updated on 11/Feb/21 $${it}'{s}\:{getting}\:{boring}! \\ $$$${please}\:{stop}\:{posting}\:{empty}\:{posts}\:{sir}! \\ $$$${try}\:{to}\:{study}\:{how}\:{to}\:{use}\:{the}\:{forum}\:{by}…
Question Number 973 by Yugi last updated on 10/May/15 $${The}\:{number}\:{of}\:{hits}\:{per}\:{minute}\:{on}\:{a}\:{website}\:{is}\:\mathrm{0}.\mathrm{8}.\:{It}\:{is}\:{shown}\:{that}\:{the}\:{time}\:{T} \\ $$$${between}\:{two}\:{successive}\:{hits}\:{follows}\:{a}\:{negative}\:{exponential}\:{distribution}\: \\ $$$${f}\left({t}\right)=\mathrm{0}.\mathrm{8}{e}^{−\mathrm{0}.\mathrm{8}{t}} \:\left(\:{t}\:\geqslant\:\mathrm{0}\:\right).\:{It}\:{is}\:{required}\:{to}\:{determine}\:{the}\:{probability}\:{that}\:{the}\:{time}\: \\ $$$${between}\:{the}\:\mathrm{1}{st}\:{hit}\:{and}\:{the}\:\mathrm{51}{st}\:{exceeds}\:{one}\:{hour}.\:{One}\:{approach}\:{to}\:{the}\: \\ $$$${calculation}\:{stated}\:{that}\:{the}\:{required}\:{probability}\:{is}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{P}\left({no}.\:{of}\:{hits}\:{in}\:\mathrm{60}\:{mins}\:<\:\mathrm{50}\right)\:\:\:\:\:\:\:\:\:\:\:\left(\:\ast\:\right) \\ $$$${Can}\:{anyone}\:{explain}\:{to}\:{me}\:{why}\:{it}\:{is}\:{that} \\ $$$${P}\left({time}\:{between}\:\mathrm{1}{st}\:{hit}\:{and}\:\mathrm{51}{st}\:{hit}\:>\:\mathrm{60}{mins}\right)=\:\left(\ast\right)\:?…
Question Number 131975 by liberty last updated on 10/Feb/21 $$\:\mathrm{Ninety}\:\mathrm{students}\:,\:\mathrm{including}\:\mathrm{Joe} \\ $$$$\mathrm{and}\:\mathrm{Jane}\:\mathrm{are}\:\mathrm{to}\:\mathrm{be}\:\mathrm{split}\:\mathrm{into}\: \\ $$$$\mathrm{three}\:\mathrm{classes}\:\mathrm{of}\:\mathrm{equal}\:\mathrm{size}\:\mathrm{and}\:\mathrm{is} \\ $$$$\mathrm{to}\:\mathrm{be}\:\mathrm{done}\:\mathrm{at}\:\mathrm{random}.\:\mathrm{What}\:\mathrm{is} \\ $$$$\mathrm{the}\:\mathrm{probability}\:\mathrm{that}\:\mathrm{Joe}\:\mathrm{and}\:\mathrm{Jane} \\ $$$$\mathrm{end}\:\mathrm{up}\:\mathrm{in}\:\mathrm{the}\:\mathrm{same}\:\mathrm{class}\:? \\ $$ Commented by liberty…
Question Number 870 by 112358 last updated on 05/Apr/15 $${In}\:{how}\:{many}\:{ways}\:{may}\:{a}\:{line}\: \\ $$$${consisting}\:{of}\:\mathrm{4}\:{men}\:{and}\:\mathrm{4}\:{women} \\ $$$${be}\:{acquired}\:{if}\:{no}\:{two}\:{women}\:{are} \\ $$$${to}\:{be}\:{adjacent}\:{to}\:{each}\:{other}? \\ $$ Answered by prakash jain last updated on…
Question Number 131828 by Salman_Abir last updated on 09/Feb/21 Answered by liberty last updated on 09/Feb/21 $$\mathrm{20}\:=\:\frac{\mathrm{6}!}{\mathrm{3}!.\mathrm{3}!} \\ $$ Commented by Salman_Abir last updated on…
Question Number 683 by 112358 last updated on 24/Feb/15 $${Determine}\:{the}\:{following}\:{sum}\:{in} \\ $$$${terms}\:{of}\:{n}. \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{S}_{{n}} =\underset{{i}=\mathrm{1}} {\overset{{n}} {\sum}}{i}^{\mathrm{2}} {q}^{{i}−\mathrm{1}} \\ $$$${where}\:\mathrm{0}\:<\:{q}\:<\:\mathrm{1}. \\ $$$${For}\:{the}\:{distribution}\:{of}\:{the}\:{discrete} \\ $$$${random}\:{variable}\:{X}\:{given}\:{as} \\…
Question Number 569 by userid1 last updated on 28/Jan/15 $$\int\:\frac{\mathrm{4}{e}^{{x}} +\mathrm{6}{e}^{−{x}} }{\mathrm{9}{e}^{{x}} −\mathrm{4}{e}^{−{x}} }\:{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 131631 by liberty last updated on 07/Feb/21 $$\mathrm{Selecting}\:\mathrm{randomly}\:\mathrm{an}\:\mathrm{integer} \\ $$$$\mathrm{from}\:\mathrm{1}\:\mathrm{to}\:\mathrm{2000}\:,\:\mathrm{find}\:\mathrm{the}\:\mathrm{probability} \\ $$$$\mathrm{that}\:\mathrm{neither}\:\mathrm{6}\:\mathrm{nor}\:\mathrm{8}\:\mathrm{divides}\:\mathrm{the} \\ $$$$\mathrm{integer}. \\ $$ Answered by som(math1967) last updated on 07/Feb/21…