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Category: Probability and Statistics

Question-192105

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-192103

Question Number 192103 by Spillover last updated on 08/May/23 Answered by otchereabdullai@gmail.com last updated on 08/May/23 $${the}\:{most}\:{important}\:{thing}\:{to}\:{know}\:{is} \\ $$$${we}\:{cant}\:{start}\:{the}\:{number}\:{with}\:{zero} \\ $$$${since}\:{is}\:{a}\:{four}\:{digit}\:{mumber}\:{without} \\ $$$${repetition} \\ $$$${the}\:{first}\:{can}\:{be}\:{chosen}\:{in}\:\mathrm{5}\:{ways},…

Question-126186

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

Question-191507

Question Number 191507 by Spillover last updated on 24/Apr/23 Answered by cortano12 last updated on 25/Apr/23 $$\left(\mathrm{a}\right)\:\underset{−\infty} {\overset{\infty} {\int}}\mathrm{f}\left(\mathrm{x}\right)\mathrm{dx}=\mathrm{1} \\ $$$$\:\:\:\:\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}}…

One-number-is-written-on-the-board-Each-time-the-number-is-either-squared-or-multiplied-bh-2-If-1-is-written-on-the-board-at-the-beginning-it-is-necessary-to-perform-at-least-several-operations-to-

Question Number 125580 by Mammadli last updated on 12/Dec/20 $$\boldsymbol{{One}}\:\boldsymbol{{number}}\:\boldsymbol{{is}}\:\boldsymbol{{written}}\:\boldsymbol{{on}}\:\boldsymbol{{the}}\:\boldsymbol{{board}}. \\ $$$$\boldsymbol{{Each}}\:\boldsymbol{{time}}\:\boldsymbol{{the}}\:\boldsymbol{{number}}\:\boldsymbol{{is}}\:\boldsymbol{{either}}\:\boldsymbol{{squared}}\:\boldsymbol{{or}}\:\boldsymbol{{multiplied}}\:\boldsymbol{{bh}}\:\mathrm{2}. \\ $$$$\boldsymbol{{If}}\:\mathrm{1}\:\boldsymbol{{is}}\:\boldsymbol{{written}}\:\boldsymbol{{on}}\:\boldsymbol{{the}}\:\boldsymbol{{board}}\:\boldsymbol{{at}}\:\boldsymbol{{the}}\:\boldsymbol{{beginning}}, \\ $$$$\boldsymbol{{it}}\:\boldsymbol{{is}}\:\boldsymbol{{necessary}}\:\boldsymbol{{to}}\:\boldsymbol{{perform}}\:\boldsymbol{{at}}\:\boldsymbol{{least}} \\ $$$$\boldsymbol{{several}}\:\boldsymbol{{operations}}\:\boldsymbol{{to}}\:\boldsymbol{{get}}\:\boldsymbol{{the}}\:\boldsymbol{{number}}\:\mathrm{2}^{\mathrm{2018}} . \\ $$ Terms of Service Privacy…

A-cord-is-drawn-at-random-in-a-given-circle-Whats-the-probability-p-that-the-cord-is-longer-than-the-side-of-an-inscribed-equilateral-triangle-in-the-circle-

Question Number 60000 by malwaan last updated on 16/May/19 $${A}\:{cord}\:{is}\:{drawn}\:{at}\:{random} \\ $$$${in}\:{a}\:{given}\:{circle}\:. \\ $$$${Whats}\:{the}\:{probability}\:\boldsymbol{{p}}\:{that} \\ $$$${the}\:{cord}\:{is}\:{longer}\:{than}\:{the}\:{side} \\ $$$${of}\:{an}\:{inscribed}\:{equilateral}\: \\ $$$${triangle}\:{in}\:{the}\:{circle}? \\ $$ Commented by mr…