Category: Probability and Statistics

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 192098 by cortano12 last updated on 08/May/23 Answered by mehdee42 last updated on 08/May/23 $$\left(c\right)\frac{6}{7}✓$$ Commented by Skabetix last updated on…

Question Number 126186 by benjo_mathlover last updated on 18/Dec/20 Commented by benjo_mathlover last updated on 18/Dec/20 $$\left(A\right)\frac{23}{257}\left(B\right)\frac{24}{257}\left(C\right)\frac{25}{257}$$$$\left(D\right)\frac{26}{257}\left(E\right)\frac{27}{257}$$ Terms of Service Privacy…

Question Number 191507 by Spillover last updated on 24/Apr/23 Answered by cortano12 last updated on 25/Apr/23 $$\left(\mathrm{a}\right)\underset{-\mathrm{\infty }}{\stackrel{\mathrm{\infty }}{\int }}\mathrm{f}\left(\mathrm{x}\right)\mathrm{dx}=1$$$$\:\:\:\:\mathrm{k}\underset{\mathrm{0}} {\overset{\mathrm{4}} {\int}}\left(\mathrm{x}^{\mathrm{2}} −\mathrm{3x}+\mathrm{4}\right)\mathrm{dx}+\underset{\mathrm{4}} {\overset{\mathrm{5}}…

Question Number 60000 by malwaan last updated on 16/May/19 $$Acordisdrawnatrandom$$$$inagivencircle.$$$$Whatstheprobability\mathit{p}that$$$$thecordislongerthantheside$$$$ofaninscribedequilateral$$$$triangleinthecircle?$$ Commented by mr…