学年

質問の種類

数学 大学生・専門学校生・社会人

確率統計の問題です。かなり難問で詳しく解説いただけると幸いです。

問5次のようなパズルのような問題がある. 問題を簡単にするために1年は365日とする (閏年は考えない). ある工場では人の工員を雇うことにする が,このうちの1人でも誕生日の人がいればその日は休みに, 1人も誕生日の人がいなければ働き、その日は 人数と同じn (単位) の利益を得るものとする。このとき,この工場の1年間の利益は働いた日数 xn にな る.例えばたまたま全員が同じ誕生日の場合は働いた日数=364 なので 364n の年間利益を得る. n人の工員をランダムに雇うとき, すなわち人それぞれの工員の誕生日は独立で一様分布に従うときこの年 間利益は確率変数になるが,その期待値を f(n) とする. この f(n) を最大にする n を求めよ. この問題は一見かなり難しいが以下の設問に沿って解答することにより f(n) を最大にする n とその時の f (n) の値を求めよ. (1) n 人の工員を雇うとき,確率変数 S を1人も誕生日の人がいない日数とするとき f(n) を S (やその期待 値, 分散など) を用いて表せ. (2) i=1,2,...,365を日にちを表すパラメータとする. 確率変数 X を次のように定める 1日に1人も誕生日の人がいなかった場合 Xi = 0日の誕生日の人がいた場合 このときP(X = 1) を求めよ. (3) (2) の設定で S を X を用いて表せ.また E[S] を求めよ. (4) 以上を用いて f(n) を具体的に表せ. (5) (4) で求めた f(n) より f(n+1)-f(n) を考えることで f (n) が最大になる n を求め, f(n) の最大値 (の 近似値)を与えよ.

回答募集中 回答数: 0
数学 高校生

465の(1)なぜθをかけているのかわからないです 最後まで解説おねがいします‪( . .)"‬

題 とき、 No. 33 正弦定理・余弦定理 ( 2 ) Date B 465 △ABCにおいて,次のものを求めよ。 (1) A: B:C=2:3:7 のとき A, B, C, a:b *(2) sin AsinB: sinC=√3:√74 のとき B sinsinsi 半解答編 -115 点Bから辺 CA に垂線 A * * * 0 <0 S 120° \45° C E B √√3)2 √3 るから 32=(3√3)2+α2-2・3√3.acos30° BH を下ろすと b=AH+CH =260 =ccos A + acos C =5√2 cos45°+10cos 30° =5+5√3 = 5(1+√3) (4)(解1)[先にaを求める] 余弦定理により,62=c2+α2-2cacos B であ これを解くと >0であるから H b. 4646-c=2から b=c+2 余弦定理により ① 03 2668 6/10 52=b2+c2-2bccos 120°+S) DA (5) ① を代入すると 30° a 52=(c+2)2+c2_2c+2ccos120° 整理して 3(c2+2c-7)=0 =-1±2/2 -√3) ゆえに a2-9a+18=0 (I) これを① に代入して これは6>0を満たすA b=1+2√2 Ta これを解いて a=3,6 [1] a=3のとき amia AS 206 AS- = A nie 余弦定理により 15° cos A=- 32+(3/3)2-32 -601 √3 2.3.3√3 三弦定理 ゆえに A=30° って C=180°--(30° + 30°)=120° [2] a=6のとき 0001 0001 00000 465 (1) A: B:C=2:3:7から A=20, B=30, C=70 とおける。 A+B+C=180°であるから (1) S=2x/20 +30 + 70 = 180° すなわち 120=180° よって 0=15° ゆえにAA=30°,B=45°,C=105° 余弦定理により お COS A である ゆえに よって 32+(3/3)2-62 A=90° 2.3.3√3 C=180° (90°+30°)=60° 正弦定理により (S) =0 8 205 ABC a: b=sinA: sin B 804 = sin 30° sin 45° =12/2 : 1 √2 . 2 以上から (2) 工法定番に a-3 1

未解決 回答数: 0
英語 高校生

英語の長文です どこに文法表現があるか知りたいです! よろしくお願いします。

5 UNIT3 Reading Passage 10 15 20 20 25 30 Listening When important events are happening around the world, most people turn to traditional media sources, such as CNN and BBC,¹ for their news. However, during the invasion of Iraq by the United States and its allies in early 2003, a significant number of people followed the war from the point of view of an anonymous² Iraqi citizen who called himself "Salam Pax" (salam means "peace" in Arabic, and pax means "peace" in Latin). Salam Pax wrote a diary about everyday life in Baghdad during the war, and posted it on his web site. Pax's online diary was a kind of web site known as a "blog." Blogs, short for "web-logs," are online diaries usually kept by individuals, but sometimes they are written by companies and other groups of people. They are a rapidly growing type of web site on the Internet. There are estimated to be several hundred thousand blogs on the Internet, and with the popularity of other social media sites, the number of people writing online about their lives continues to grow. may find A blog differs from a traditional web site in several ways. Most importantly, it is updated much more regularly. Many blogs are updated every day, and some are updated several times a day. Also, most blogs use special software or web sites which are specifically aimed at bloggers, so you do not need to be a computer expert to create your own blog. This means that ordinary people who computers difficult to use can easily set up and start writing their own blog. In 2003, the Internet company AOL³ introduced their own blogging service, enabling its 35 million members to quickly and easily start blogging. There are many different kinds of blogs. The most popular type is an online diary of links, where the blog writer surfs the Internet and then posts links to sites or news articles that they find interesting, with a few comments about each one. Other types are personal diaries, where the writer talks about their life and feelings. Sometimes these blogs can be very personal. There is another kind of blogging, called "moblogging," short for "mobile blogging." Mobloggers use cell phones to take photo's, which are posted instantly to the Internet. When the content and images posted online involve news subjects, mobloggers become citizen journalists. In fact, the Korean web site OhMyNews was a well known source for articles from international citizen journalists. However, in 2010, OhMyNews stopped posting new articles. Instead, it is now a blog site where citizen journalists can choose what makes the headlines, or just share ideas about how regular people are changing the news world. Anyone who visits the web site of a big media company can clearly see how the idea of blogging has changed the reporting of news. Quite often, a list of reader comments follow news articles. It seems that the news is becoming less like a report or a lecture, and more like a conversation, where anyone can join in. CNN, BBC Cable News Network, British Broadcasting Corporation anonymous not named; unknown 3 AOL America Online

回答募集中 回答数: 0