Category: Probability and Statistics

Question Number 10714 by Saham last updated on 23/Feb/17 $$\mathrm{Given}\mathrm{the}\mathrm{following}\mathrm{information}\mathrm{regarding}\mathrm{the}\mathrm{follwing}$$$$\mathrm{distribution}:$$$$\mathrm{n}=5,\stackrel{-}{\mathrm{x}}=10,\stackrel{-}{\mathrm{y}}=20,\mathrm{\Sigma }{(\mathrm{x}-4)}^2=100,\mathrm{\Sigma }{(\mathrm{y}-10)}^2=160,$$$$\mathrm{\Sigma }(\mathrm{x}-4)(\mathrm{y}-10)=80$$$$\left(\mathrm{i}\right)$$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{two}\:\mathrm{regression}\:\mathrm{coefficient}\:\mathrm{and} \…

Question Number 141633 by Willson last updated on 21/May/21 $$1<\mathrm{a}<\mathrm{b},\mathrm{prove}\mathrm{that}:$$$${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 $$\mathrm{Prove}\mathrm{that}$$$$\mathrm{\forall }\mathrm{n}\in \mathbb{N}{\underset{\mathrm{n}}{\int }}^{\mathrm{n}+1}\mathrm{lnt}\mathrm{dt}⩽\ln (\mathrm{n}+\frac{1}{2})$$ 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 $$\mathrm{A}\mathrm{fair}\mathrm{die}\mathrm{is}\mathrm{thrown}4\mathrm{times}.\mathrm{What}\mathrm{is}\mathrm{the}$$$$\mathrm{probability}\mathrm{of}\mathrm{obtaining}\mathrm{a}6\mathrm{twice}?$$ Answered by MJS last updated on 17/Dec/19 $$\frac{1}{6}\times \frac{1}{6}\times \frac{5}{6}\times \frac{5}{6}\times \left(\begin{array}{c}4\\ 2\end{array}\right)=\frac{25}{216}\approx 11.57\mathrm{\%}$$ Commented…

Question Number 10116 by Gaurav3651 last updated on 25/Jan/17 $$whatistheprobabilityof5sundays$$$$inthemonthofdecember?$$ Commented by prakash jain last updated on 25/Jan/17 $$\mathrm{Favorable}\mathrm{cases}-1\mathrm{dec}$$$$\mathrm{1}\:\mathrm{dec}\:\mathrm{Sunday}\Rightarrow\mathrm{1},\mathrm{8},\mathrm{15},\mathrm{22},\mathrm{29}\:\mathrm{are}\:\mathrm{sundays}…