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Category: Probability and Statistics

find-integers-x-y-such-that-x-x-3-4-y-2-45-1-100-

Question Number 212926 by efronzo1 last updated on 27/Oct/24 $$\:\mathrm{find}\:\mathrm{integers}\:\mathrm{x},\mathrm{y}\:\mathrm{such}\:\mathrm{that}\: \\ $$$$\:\:\:\frac{\mathrm{x}}{\mathrm{x}−\mathrm{3}}\:−\frac{\mathrm{4}}{\mathrm{y}^{\mathrm{2}} −\mathrm{45}}\:=\:\frac{\mathrm{1}}{\mathrm{100}} \\ $$ Answered by Frix last updated on 27/Oct/24 $$\Leftrightarrow \\ $$$${x}=\frac{\mathrm{3}\left({y}^{\mathrm{2}}…

The-expected-number-of-values-drawn-fromthe-interval-0-1-at-random-if-the-sum-ofthe-values-drawn-so-far-is-less-than-1-is-too-cntinue-drawing-what-is-the-expectede-numbr-of-draws-

Question Number 212918 by MrGaster last updated on 26/Oct/24 $$\mathrm{The}\:\mathrm{expected}\:\mathrm{number}\:\mathrm{of}\:\mathrm{values}\:\mathrm{drawn}\: \\ $$$$\mathrm{fromthe}\:\mathrm{interval}\left[\:\mathrm{0}\:,\mathrm{1}\right]\:\mathrm{at}\:\mathrm{random}\:\mathrm{if}\:\mathrm{the}\:\mathrm{sum}\: \\ $$$$\mathrm{ofthe}\:\mathrm{values}\:\mathrm{drawn}\:\mathrm{so}\:\mathrm{far}\:\mathrm{is}\:\mathrm{less}\:\mathrm{than}\:\mathrm{1},\:\mathrm{is}\:\mathrm{too} \\ $$$$\mathrm{cntinue}\:\mathrm{drawing}\:\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{expectede} \\ $$$$\mathrm{numbr}\:\mathrm{of}\:\mathrm{draws} \\ $$ Terms of Service Privacy Policy…

Q-The-collection-A-12-13-15-18-23-24-25-26-amp-B-A-if-m-M-B-m-min-amp-M-max-amp-nm-10k-which-number-of-B-1-59-2-60-3-61-4-62-

Question Number 209732 by MM42 last updated on 19/Jul/24 $$\left.{Q}\right)\:{The}\:{collection}\:{A}=\left\{\mathrm{12},\mathrm{13},\mathrm{15},\mathrm{18},\mathrm{23},\mathrm{24},\mathrm{25},\mathrm{26}\right\}\&\:{B}\subseteq{A} \\ $$$${if}\:\:{m},{M}\:\in{B}\:\:;\:{m}={min}\:\&\:{M}\:={max}\:\&\:\:{nm}=\mathrm{10}{k} \\ $$$${which}\:{number}\:{of}\:\:{B}\:: \\ $$$$\left.\mathrm{1}\left.\right)\left.\mathrm{5}\left.\mathrm{9}\:\:\:\:\:\:\:\mathrm{2}\right)\mathrm{60}\:\:\:\:\:\:\:\mathrm{3}\right)\mathrm{61}\:\:\:\:\:\:\mathrm{4}\right)\mathrm{62} \\ $$$$ \\ $$ Answered by mr W last…

three-points-are-randomly-selected-on-a-circle-to-form-a-triangle-1-find-the-probability-that-the-center-of-the-circle-lies-inside-the-triangle-2-find-the-probability-that-the-triangle-is-an-acu

Question Number 209510 by mr W last updated on 12/Jul/24 $${three}\:{points}\:{are}\:{randomly}\:{selected} \\ $$$${on}\:{a}\:{circle}\:{to}\:{form}\:{a}\:{triangle}.\: \\ $$$$\left.\mathrm{1}\right)\:{find}\:{the}\:{probability}\:{that}\:{the}\:{center} \\ $$$${of}\:{the}\:{circle}\:{lies}\:{inside}\:{the}\:{triangle}. \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{probability}\:{that}\:{the}\: \\ $$$${triangle}\:{is}\:{an}\:{acute}\:{triangle}. \\ $$ Terms of…

Question-209424

Question Number 209424 by Tawa11 last updated on 09/Jul/24 Commented by Tawa11 last updated on 09/Jul/24 $$\mathrm{In}\:\mathrm{this}\:\mathrm{kind}\:\mathrm{of}\:\mathrm{probability},\:\mathrm{is}\:\mathrm{the}\:\mathrm{formular}. \\ $$$$\mathrm{p}\left(\mathrm{x}\:=\:\mathrm{r}\right)\:\:=\:\overset{\mathrm{n}} {\:}\mathrm{C}_{\mathrm{r}} \:\mathrm{p}^{\mathrm{r}} \:\mathrm{q}^{\mathrm{n}\:−\:\mathrm{r}} \\ $$$$\mathrm{or} \\…

Question-209031

Question Number 209031 by Spillover last updated on 30/Jun/24 Answered by Spillover last updated on 07/Jul/24 $${f}\left({x}\right)=\begin{cases}{\frac{\mathrm{1}}{{n}}\:\:\:\:{x}=\mathrm{1},\mathrm{2},\mathrm{3},…..=\frac{\mathrm{1}}{{n}}\left[{e}^{{t}} +{e}^{\mathrm{2}{t}} +{e}^{\mathrm{3}{t}} +……..\right]}\\{\mathrm{0}\:\:{else}\:{where}}\end{cases} \\ $$$$\left({a}\right)\:{moment}\:{generating}\:{function} \\ $$$${M}_{{x}} \left({t}\right)={E}\left({e}^{{tx}}…