確率の勉強をしている学生なのですが、この問題が分かりません。どなたか教えていただけませんか。

練習問題 1.8 (積率母関数) X を非負の確率変数とし, x(t) = Eetx は全てのt∈ に対して有限であると仮定する.さらに,全てのt∈ R に対し E [XetX] < ∞ であると仮定する.この練習問題の目的は, '(t) = E [Xetx] で あり、特に'(0)=EX であることを示すことである。 微分の定義, すなわち次式を思い出そう. 4'(t) = lim x(t) - (s) lim st t-s st EetxEesx t-s 「etx = lim E st t-s 上式の極限は,連続な変数sについて取っているが,t に収束する実数列{8}n=1を 選ぶことができ, 次を計算すればよい. 「etx e³n X lim E sn→t t-Sn これは、次の確率変数の列 etx -enx Yn = t-Sn の期待値の極限を取っていることになる.もしこの極限が, t に収束する列{Sn}=1 の選び方によらず同じ値になるならば、この極限も limotE [ex と同じで,そ れは '(t) である. .tx sx ← -e t-s 解析学の平均値の定理の主張は,もしf(t) が微分可能な関数ならば、任意の実数 s ともに対し,stの間の値の実数0で次を満たすものが存在するというものである. f(t)-f(s) =f' (0) (t-s). もしweΩを固定し,f(t) = etx(w) を定義すると,この式は, etX(w)_esx(w)=(t-s) X (w)e (w)x(w) (1.9.1) となる.ただし,(ω) はωに依存する実数 (すなわち,tとsの間の値を取る確率変 数)である. (i) 優収束定理 (14.9) (191) 式を使って,次を示せ. lim EY = Elim Yn=E [XetX] . (1.9.2) n→∞ [n→∞ このことから,求める式 4'(t) [XetX ] が導かれる. (ii) 確率変数 X は正の値も負の値も取り得、全てのt∈Rに対し Eetx < かつ E [|X|etX] < ∞ であると仮定する。 再度 '(t) = E [XetX] を示せ(ヒント: (1.3.1) 式の記号を使って X = X + - X- とせよ . )

informations···▸informationに変えるような問題です。 答え合わせがしたいので、答えを教えて頂きたいです。大問1と2です。

1 Correct the sentences which have mistakes. Tick (✔) the correct sentences. 1 Do you have any informations about these people? information 2 How many people do you employ? Sorry, I don't have much time. Let's be quick. 4 A little customers have complained about the increase. 5 I'm afraid we don't have many paper in stock. 6 There isn't much demand for this line any more. Give him any more time to finish this. I've got fewer space in my new office than in my old one. 9 A lot of people said they preferred the taste of this one. 10 I'd like a little help with that, please. 7 8 2 Two people are checking the store cupboard at work. Complete their conversation with a suitable quantifier. A So, how many boxes of paper clips do we have in stock? so we should B Well, we only have a ² probably order some more. A How about ink cartridges? I don't think there are left. 3 B Well, there's an extra box of them here, but we'll more, sooner or later. need 4 A OK. What about the coffee machine? How 5 coffee is there? B There's a 6 7 of that, but there aren't packets of tea. A Right, so that's paper clips, ink cartridges and tea. Anything else? a at the moment, but people in the office have asked me if B Well, we don't have 8 9 we can have biscuits for the tea breaks.

答え合わせの為、答えを教えて頂きたいです。 よろしくお願いします。ビジネス英語です。

Working with words 1 Complete the sentences with the words in bold. Change the form of the word in bold or add another word to it. supply 1 It's important to build good relationships with different suppliers. 2 Our supply chain begins with the manufacturer in India and ends in our UK shops. is much higher but it's transport 3 The cost of air faster. show 4 Customers from all over Europe visit our in Paris and Milan. invent 5 Every item in our photographic records of each of them. middle 6 The problem with using is that it adds to the final cost of products because we have to add on their fee. is unique, so we keep ship 7 We have a large. track 8 We use barcodes to stock coming in and out of the warehouse. made 9 All our pots are _, which makes them expensive, but our target customer doesn't want anything mass-produced. original 10 The arriving in three days. of the of the products is printed on the bottom of the box. 2 Underline the correct words in italics to complete the sentences. 1 The book is currently out of stock, but it is on / out of order, so we'll have it soon. 2 We need to stock up on / run out of headed paper. Could you put an order in? 3 I ran low on/out of ink, so I couldn't print out the report. 4 We can keep track of/ on track our order by satellite. 5 Let's stop at the next service station. We are running low/out on petrol. Business 1 Complete the phone call between Virginie, a customer, and Kevin, a call handler. Put the words in italics in the correct order. Kevin Good afternoon, you're speaking to Kevin. How can I help you? Virginie Hello, I am up/chasing/an/order chasing up an order I placed three weeks ago. Kevin account /take/I/your/details / Can please? 2 Virginie Yes. The account number is 572638. Kevin OK. If you bear with me a moment, I'll into / look/it 3 Let me see. Well, my /to / information / according it is still on order. 4 Virginie I really need to know happened /to/has/it/ what 5 Could check/me/you/it/for/out 6 ? Kevin Certainly. I'll back/you/to/hour / within/get/ the 7 Virginie Thank you. 2 Kevin calls Virginie back. Complete their conversation with the phrases from the list. put the order straight through asap charge it to was dispatched on check it out as quick as we can must have gone wrong Kevin Hello, this is Kevin from DYK calling. I've got some information about your order. Virginie Oh, thanks for calling back. So, what's happened to it? Kevin Well, we put the order straight through to the warehouse, and it 2_ the 25th. Virginie But I haven't received it yet. Kevin I'm sorry about that. Can you confirm the delivery address? Virginie We wanted it delivered to our Brussels office. Kevin Oh, something 3 It looks like it might have gone to your Paris office instead. I'll 4 straightaway. Virginie I've already been waiting three weeks. Could you just send it again 5 ? Kevin OK, no problem. We'll resend it Virginie Thank you. And please not the Paris one. the Brussels account,

これ読んだんですけど、自分は世界史を理解してなかったので分からなくて翻訳アプリ使ったんですけどそれでも分からなかったので分かる方できれば解読お願いします┏●

Denmark in World War II お んれ By Hannah Arendt Hannab Arendt (1906-1975) was a political scientist! and pbilosopber born in Hanover, Germany. Wben Hitler came to power, sbe was forced to leave Germany and came to the United States in 1940. Sbe continued ber academic career by lecturing and teacbing at arious colleges, including The New Scbool for Social Researcb in New York City. Among the many books sbe urote were Eichmann in Jerusalem, On Revolution, and The Origins of Totalitarianism. Editor's Insert During the Second World War. the Germans invaded Denmark in April, 1940. In the beginning of her essay, Hannah Arendt explains that of the four countries almost completely immune to anti-Semitism- Denmark, Sweden, Italy, and Bulgaria Denmark challenged its German masters directly. As soon as the German authorities talked about forcing Jews to wear the yellow badge,' the Danes replied that all Danish citizens, including the King, would be wearing it the next day if the policy were carried out. In addition, all Danish government officials threatened 舌は the German authorities with their immediate resignation if the Germans started to implement any anti-Jewish actions. The following excerpt from Eicbmann in Jerusatem shows how the Danes sabotaged the German plan to carry out the mass extermination of the Jews. only 2タカ人の What happened then was truly amazing; compared with what took place in other European countries, everything went topsy-turvey. In August, ー after the German offensive in Russia had failed, the Afrika Korns 1943 had surrendered in Tunisia, and the Allies had invaded Italy すgovernment canceled its 1940 agreement with Germany which had permitted German troops the right to pass through the country. Thereupon. the Danish workers decided that they could help a bit in hurrying things そのうえに up: riots broke out in Danish shipyards, where the dock workers refused to repair German ships and then went on strike. The German militarv commander proclaimed a state of emergency and imposed martial la and Himmler thought this was the right moment to tackle the Te the Swedish す。 (continued on next page) themselves as Jews secret police), and overseer of the concentration camps

問2の(3)(4)を教えてください

問2. ばね定数 k [N /m] (k > 0) の軽いばねがある。なめらかな水平面上でこ 自然長 のばねの左端を固定し、右端に質量 m kg] の物体を取り付けた。次に、 手で mm 物体を引っ張ってばねを自然長より cm 伸ばしてから静かに手を放した。図 0 に定義された座標軸に基づいて、その後の物体の運動について、以下の間に答 えよ。ただし,時刻 ts]での物体の位置を (t) [m] とし、ばねが自然長のときの物体の位置を原点とする。 (1) Find the restoring force F, [N] that the spring tries to return when the object is displaced by z m from its natural length. (2 points) d'z as its acceleration. dt? (2 points) (2) Find the equation of motion of the object, using the notation of (3) Find the general solution of the equation of motion of the object. (3 points) (4) Find the solution that meets the initial conditions described in the problem. Here, the moment when the hand is released is set as time t==0s. (3 points) 問3.問2では摩擦などの抵抗力がない理想的な単振動を扱ったが、実際には抵抗力が存在する。 抵抗力は速度 dt に比例することが多く、この比例定数をc[N.s/m] (c> 0) とおくと、 運動方程式は教科書 P.66 の(2.40)式として表 される。この方程式の一般解は、 教科書 P.52に示す「定数係数の2階線形同次微分方程式の一般解」として表され、 教科書 P.66 の下段3行に示すような解 a) c)となる。これらの解の導出課程を、 以下の手順に従って示せ。 d。 da. (1)(2.40)式 m = ーkc - c dt? の右辺において、c dt の項の符号がマイナスである理由を考察せよ。 dt (2点)

問2の(3)(4)を教えてください

問2. ばね定数 k [N /m] (k > 0) の軽いばねがある。なめらかな水平面上でこ 自然長 のばねの左端を固定し、右端に質量 m kg] の物体を取り付けた。次に、 手で mm 物体を引っ張ってばねを自然長より cm 伸ばしてから静かに手を放した。図 0 に定義された座標軸に基づいて、その後の物体の運動について、以下の間に答 えよ。ただし,時刻 ts]での物体の位置を (t) [m] とし、ばねが自然長のときの物体の位置を原点とする。 (1) Find the restoring force F, [N] that the spring tries to return when the object is displaced by z m from its natural length. (2 points) d'z as its acceleration. dt? (2 points) (2) Find the equation of motion of the object, using the notation of (3) Find the general solution of the equation of motion of the object. (3 points) (4) Find the solution that meets the initial conditions described in the problem. Here, the moment when the hand is released is set as time t==0s. (3 points) 問3.問2では摩擦などの抵抗力がない理想的な単振動を扱ったが、実際には抵抗力が存在する。 抵抗力は速度 dt に比例することが多く、この比例定数をc[N.s/m] (c> 0) とおくと、 運動方程式は教科書 P.66 の(2.40)式として表 される。この方程式の一般解は、 教科書 P.52に示す「定数係数の2階線形同次微分方程式の一般解」として表され、 教科書 P.66 の下段3行に示すような解 a) c)となる。これらの解の導出課程を、 以下の手順に従って示せ。 d。 da. (1)(2.40)式 m = ーkc - c dt? の右辺において、c dt の項の符号がマイナスである理由を考察せよ。 dt (2点)

英語進行形の問題です。 答えがないので合ってるか教えていただけると嬉しいです… よろしくお願いします🙇‍♂️

これったた tcedo aidt m16 Challenge Bnec fenigino GS92 S a0 Fill in the blanks with the appropriate word(s) to complete the sentences. o obJed この日たて at the moment. 1. The weight scale broke down yesterday ánd is Obeing repaired © repaired getting a second opinion from another specialist. 2 am thinking of ③ think の having repaired ③ having been repaired 2. I O am thinking の have thought どうにっなんと。 talkative now. 3. Todd is nóormally the quietest in the group, but sómehow he (@is being のwill be O has been 3 was - 種の。神縁 4. John is sort of neurótic: he is always going to hospital and diseases. over imaginary O is worried 2/worries ③ worried ④ worrying

英語全然わかりません。 助けてください。 お願いします。 訳してください。

Any person who goes abroad is probably surprised at the strength of his main own nationalistic feelings, but Japanese are less able than most others to lose the 5 consciousness of their national origins even momentarily and are more likely to lang see themselves always, not just as representing themselves, but as somehow being tow exemplars of the whole Japanese nation. A Japanese who distinguishes himself in Wi! the world is much less likely to think of himself or be thought of by his friends sh and acquaintances as little Taro Yamamoto who made good, but as a Japanese who 10 th became famous. In the Olympics, with its raising of national fags and playing of W national anthems, the nationalism of all participants is fanned, but at least those ti from the Western democracies usually feel a sense of personal achievement much J more and the burden of national honor much less than do Japanese participants. The strength of these Japanese attitudes has created special problems for 15 those Japanese who migrate abroad. When Japan went to war with the United

What invariably～の所の(2)についてです refuse move choose lose ariseのどれかが入るのですがchooseが入ります。 私はmoveだと思ったのですがchooseのが入る理由が分からなく解説見てもいまいち分かりません

We have all experienced days When everything gOeS WTOnP. A day may begin well enough, bt suddenly everything Seermns tO ( 1 ) out of control. What invariably happens is that a great JnVarii number of things ( 2 ) to go wrong 8t precisely the same 30 s moment. It is as 詳 a single unimportant eVent Set UD 4 chain of reactions. Let us ( 3 ) that you are preparing a meal and keeping an eye on the baby at the same tme. The telephone rings and this

青のマーカーを引いたところで、that節がなぜsomethingにかかるとわかるのですか？

1 99 まるで一のように] まさに Marcus Aurelius.Roman emperor and philosopher. Tf 1本荒えがある」 ee RET ー 1 ing more Or lesi 「今を 3 t we Ting, it iS becauSe philosophers and religlOUS thinkers haVe been Say1ng pn 二 S SN NN ts ーー コ る。 DR こい the same thing fron time Gmmemorial). ・明らかに W る! Aa 19ぇ cannot 7e ere 7の地 1 も seriQ pe er 7がの24 het ア/ye 7 7の6 7656777 (To・ 急 Clearly we human beings must haVe great difficulty HiVing mindfully in the : -ヒ=ゴ have difficulty (ぞ) on 「"す るのに大する まこ Present. | why 本 so many philosophers feel the need to keep reDeatmg om 民もし) そうでなければ」 人《仮定法週去% WW the message? 罰 sound 古落| ほ) "問題提紀 ド は d now] does not 選 On the face of it [fully cngaging the here am El ma 。紅 5 有lつを生さる]ご fel6 ce is right here in front of us. And it iS 7のW right noWi 国 what the : RS ! ・表面上は. 今この引 problem? 1 す BE 時 き heは い。何が問題なのか 電 Some people drift away from the present (by desiring something (better than < 55mepeople -. Others … 「ごする人もいる・ (に方で) …する人もいる | ( 誰妥 what exists here and now). @琶 drift away into cwWwhats nex?” Another。 more 1 > Ss [今を生きる| ことがで full immersion in the present iS by seeing all of Hfe as ! 'ない人々| V C ・現寿に没頭できなQA&G 語 preparing fOr dinner 箇 preparing forlifeinthe : は様々なタイプがある to B IAからB に及! ! >xams 個l8 somewhcre iDeWeen. SN 「中間に] [その反対に} ! of (who persistently dwell in the past。、with Rem eitherAorBorG ) 回 原本 ss 旧We can always 台8gime our hves 明 different jmagine O as C 「O がCだと旨像する] 2 4 人は想像力や拡張された記 always see alternatives. Apparently, 衣により, 現実にMDる 生を想像し、 過去の人生 上 to resis0. 男RSM語, we can remember 人 す [同様に! 才 これ5 ご 、 これらは抵抗し著いも0記 語本| also seems irresistible.