Category: Probability and Statistics

Question Number 141633 by Willson last updated on 21/May/21 $$\mathrm{1}<\mathrm{a}<\mathrm{b}\:,\mathrm{prove}\:\mathrm{that}\:: \\ $$$${b}^{{n}} \:=\:\underset{{k}=\mathrm{0}} {\overset{{n}} {\sum}}\left(−\mathrm{1}\right)^{{k}} \mathrm{C}_{{n}} ^{{k}} \:{a}^{\frac{{ln}\left(\underset{{p}=\mathrm{0}} {\overset{{n}−{k}} {\sum}}\mathrm{C}_{{n}−{k}} ^{{p}} {a}^{{n}−{p}} {b}^{{p}} \right)}{{ln}\left({a}\right)}} \\…

Question Number 141409 by Willson last updated on 18/May/21 $$\mathrm{Prove}\:\mathrm{that}\: \\ $$$$\forall\mathrm{n}\in\mathbb{N}\:\:\:\:\underset{\mathrm{n}} {\int}^{\:\mathrm{n}+\mathrm{1}} \mathrm{lnt}\:\mathrm{dt}\:\leqslant\:\mathrm{ln}\left(\mathrm{n}+\frac{\mathrm{1}}{\mathrm{2}}\right) \\ $$ Answered by TheSupreme last updated on 19/May/21 $$\int{ln}\left({t}\right)={xln}\left({t}\right)−{x} \\…

Question Number 75802 by pete last updated on 17/Dec/19 $$\mathrm{A}\:\mathrm{fair}\:\mathrm{die}\:\mathrm{is}\:\mathrm{thrown}\:\mathrm{4}\:\mathrm{times}.\:\mathrm{What}\:\mathrm{is}\:\mathrm{the} \\ $$$$\mathrm{probability}\:\mathrm{of}\:\mathrm{obtaining}\:\mathrm{a}\:\mathrm{6}\:\mathrm{twice}? \\ $$ Answered by MJS last updated on 17/Dec/19 $$\frac{\mathrm{1}}{\mathrm{6}}×\frac{\mathrm{1}}{\mathrm{6}}×\frac{\mathrm{5}}{\mathrm{6}}×\frac{\mathrm{5}}{\mathrm{6}}×\begin{pmatrix}{\mathrm{4}}\\{\mathrm{2}}\end{pmatrix}\:=\frac{\mathrm{25}}{\mathrm{216}}\approx\mathrm{11}.\mathrm{57\%} \\ $$ Commented…

Question Number 10116 by Gaurav3651 last updated on 25/Jan/17 $${what}\:{is}\:{the}\:{probability}\:{of}\:\mathrm{5}\:{sundays} \\ $$$${in}\:{the}\:{month}\:{of}\:{december}? \\ $$ Commented by prakash jain last updated on 25/Jan/17 $$\mathrm{Favorable}\:\mathrm{cases}−\:\mathrm{1}\:\mathrm{dec} \\ $$$$\mathrm{1}\:\mathrm{dec}\:\mathrm{Sunday}\Rightarrow\mathrm{1},\mathrm{8},\mathrm{15},\mathrm{22},\mathrm{29}\:\mathrm{are}\:\mathrm{sundays}…

Question Number 75538 by mhmd last updated on 12/Dec/19 Terms of Service Privacy Policy Contact: info@tinkutara.com