SCENARIO 8-3 To become an actuary, it is necessary to pass a series of 10 exams, including the most important one, an exam in probability... 繼續閱讀

統計～ 請問a.b小題要怎麼解🙏🙏

a. 4. The Boston Fire Department receives 911 calls at a mean rate of 1.6 calls per hour. Suppose the number of calls per hour follows a Poisson probability distribution. What is the probability that there will be less than one hour between 911 calls? b. What is the probability that there will be 30 minutes or more between 911 calls? c. What is the probability that there will be more than 5 minutes, but less than 20 minutes between 911 calls?

求解答案是否正確

Multiple-choice questions: (70 points) write the letter of statement that is not true: 1. A.B.U The Drude Model: (a) It is a classical approach using concepts from the kinetic theory of gases. (b) A relaxation-time approximation is used where the probability of collision is l/t. (c) No forces act on the electrons in between collisions. (d) It predicts accurately the electronic heat capacity of metals. 2. The Sommerfeld Model: (a) The crystal potential is replaced by an average Coulomb potential. (b) The separation of states is so close that a continuum model can be applied. (c) The electrons are highly localized due to a strong crystal potential. (Q) The energy of the highest occupied state at 0 K is the Fermi energy. 3. Density of states in k-space, N(k): (a) N(k) is determined by the boundary value conditions. (b) For lattices in any dimensions, N(k) is constant in k-space. (C) N(k) depends on the direction and magnitude of k. (d) It is directly proportional to the volume of the crystal. E影響, c 4. The Fermi surface of a metal: (a) is responsible for many of the transport properties of the metal, (b) depends on the nature of the chemical bonds, (c) is always a sphere, (d) can involve mixing of electron orbitals. ✓ 5. The conductivity of a material () increases with the mobility of its carriers, (b) increases with the density of carriers, (C) it is inversely proportional to the energy gap. cogu changes with temperature. 6. BID Plasmons: (a) They are an important characteristic of the Sommerfeld electron gas model. (b) Plasmons occur spontaneously in metals. (c) They are related to charge density oscillations. (d) The Plasmon energy is typically of the order of 10 eV. The Fermi energy Ef in intrinsic semiconductors 8) is usually close to y E, at OK (b) it ACiD. can increase or decrease with temperature depending on the ratio of hole and electron effective masses, (c) it represents the point at which the probability of occupation is 12, even though there may not been any states with that energy, (d) its value relative to the electronic bands must remain unaffected in the presence of defects or interfaces.

求解第30、31題

演練題(Q&A) 4.機率分配模型 D: P(X> 8) C : 49/12 Ans C Ans c D: 3.5 31 標準常態分配的四分位距(IQR)約為多少? z 27:令為指數分配之隨機變數目變異數ar(X)=4,則平均數 EIN) = ? A:4 E(X)= =12 I # B: 16 C:2 Ans C D: 8 Varlx) = 7 7 7 =4 , 1 - 1 - 2 1.2 28:令X為平均數 ECK)=3 之指數分配隨機變數,則變異數 Var(N) = ? A:3 E(X) = 1 = 3.1= Standard Normal table: probability for PGO <Z <z) 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.0 | 0.0000 0.0040 0.0080 0.0120 0.0160 0.0199 0.0239 0.0279 0.0319 0.0359 0.1 0.0398 0.0438 0.0478 0.0517 0.0557 0.0596 0.0636 0.0675 0.0714 0.0753 0.3 0.1179 0.1217 0.12550.1293 0.1331 0.1368 0.1406 0.1443 0.1480 0.1517 0.4 0.1554 0.1591 0.1628 0.1664 0.1700 0.1736 0.1772 0.1808 0.1844 0.1879 0.5 0.1915 0.1950 0.1985 0.2019 0.2054 0.2088 0.2123 0.2157 0.2190 0.2224 0.6 0.2257 0.2291 0.2324 0.2357 0.2389 | 0.2422 10.2454 | 0.2486 0.2517 0.2549 0.8 0.2881 0.2910 0.2939 0.2967 0.2995 0.3023 0.3051 0.3078 0.3106 03133 0.9 0.3159 0.3186 0.3212 0.3238 0.3264 0.3289 0.3315 0.3340 0.3365 0.3389 1.0 0.3413 0.3438 0.3461 0.3485 0.3508 0.3531 0.3554 0.3577 0.3599 0.3621 1.1 0.3643 0.3665 0.3686 0.3708 0.3729 0.3749 0.3770 0.3790 0.3810 0.3830 0.3849 0.3869 0.3888 0.3907 0.3925 0.3944 0.3962 0.3980 0.3997 0.4015 1.4 0.4192 0.4207 0.4222 0.4236 0.4251 0.4265 0.4279 0.4292 0.4306 0.4319 1.5 0.4332 0.4345 0.4357 0.4370 0.4382 0.4394 0.4406 0.4418 0.4429 0.4441 1.610.4452 | 0.4463 0.4474 0.4484 0.4495 0.4505 0.4515 0.4525 0.4535 0.4545 1.7 0.4554 0.4564 0.4573 0.4582 0.45910.4599 0.4608 0.4616 0.4625 0.4633 1.9 0.4713 0.4719 0.4726 0.4732 0.4738 0.4744 0.4750 0.4756 0.4761 0.4767 2.0 | 0.4772 0.4778 0.4783 0.4788 0.4793 0.4798 0.4803 0.4808 0.4812 0.4817 2.2 | 0.4861| 0.4864 10.4868 | 0.487110.48TS | 0.4878 10.4881| 0.4884 0.4887 0.4890 2.3 0.4893 0.4896 0.4898 0.4901 0.4904 0.4906 0.4909 0.4911 0.4913 0.4916 2.4 0.4918 0.4920 0.4922 0.4925 0.4927 0.4929 0.4931 0.4932 0.4934 0.4936 2.5 0.4938 0.4940 0.4941 0.4943 0.4945 0.4946 0.4948 0.4949 0.4951 0.4952 2.6 0.4953 0.4955 0.4956 0.4957 0.4959 0.4960 0.4961 0.4962 0.4963 0.4964 2.7 0.4965 0.4966 0.4967 0.4968 0.4969 0.4970 0.49710.49720.4973 0.4974 12.9 | 0.4981| 0.4982 | 0.4982 | 0.4983 | 0.4984 | 0.4984 | 0.4985 | 0.4985 | 0.4986 | 0.4986 0.4987 0.4987 0.4988 0.4988 0.4989 0.4989 0.4989 0.4990 0.4990 0.4991 0.4991 0.4991 0.4992 0.4992 0.4992 0.4992 0.4993 0.4993 3.3 0.4995 0.1995 0.4995 0.4996 0.4996 0.1996 0.4996 0.4996 0.4996 0.1997 0.4997 0.4997 0.4997 0.4997 0.4997 0.4997 0.4997 0.4997 0.4998 B:6 C:9 Vaulx) = 2 D:1 Ansc Aie? 29:令X為平均數 EX)=3 之指數分配隨機變數,則機率 PK > 6) = ? -AX 大 tits e B:1-e' -2x Ciel M-3, M = 3 he LLLLLL 3.0 0.4987 3.1 0.4990 # Nah l-e 3.4 0.4997 Die Ans A A:1 B: 1.5 30 : 令X為平均數E(X)=4之指數分配隨機變數,則條件機率 PK >6|Y>2) = ? A: P(X>6) C: 1.34 Pl (x>6) (x > 2)) P(X>6) P( X2) D: 2 B: P(X> 2) 4 4 P(X>2) e C: P(x > 4) Ansc

機率 答案是0.3946求過程

6.45 At a train reservation counter, one man com- pletes his reservation with a mean time of 3 minutes. Service completion time is assumed to follow exponen- tial distribution. Out of the 5 customers in queue, what is the probability that at least 4 will complete their reservation within 3 minutes? t

想請問是怎麼從第三個等號跳到第四個等號的，推了好久還是推不出來QQ 求那一步的詳細過程，感謝🙏

If X is a geometric random variable, show analytically that PX = n + k|X> n = PX = k Using the interpretation of a geometric random variable, give a verbal argument as to why the preceding equation is true. flacomath 5.0 0 1 Let X distribute geometric with success probability p, and failure probability q=1, p. Then, - P(X = n +k and X > n) P(X = n + k|X > n) = P(X > n) P(X = n + k) 1- P(X <n) qn+k-1p 1-21-1 q-1p qn+k-1p qn+k-1p q" - - =qk-1p = P(X = k)

第二題的d的積分範圍要怎麼設

6 Kx, lo, 14) 1. (10 points) How many even numbers can be formed from the digits 9, 1,4,5,6, and 9 if each digit can be used only once? 2. (50 points) Let X and Y denote the lengths of life, in years, of two components A and B, respectively, ş! x2 in an electronic system. If the joint density function of these variables is 64 0<x<1-ycl EX,Y) Rx hy 0 < x <1.0<x<1-x: f(x, y) = elsewe jey.301-4)*84f CX74 3 Rxdy * 了 1' Jay You Determine the value k; FED ECX) = 86 x 6xci->)dy cy) 3(1-2) ² (b) Find the marginal distributions, expected values, variances, and covariance of X and Y; dy= 1 (C) Determine whether X and Y are dependent or independent; X(d) Find the probability that the length of life of component A is less than that of component B; X(e) Find the probability that the length of life of component A is greater than one year, given the ar length of life of component B is equal to two year. xcy 1313. (10 points) The probability that a flight departs on time is 0.3; the probability that it arrives on time is 0.3; and the probability that it departs and arrives on time is 0.1. Find the probability that it arrives on time, given that it did not depart on time. ex oin 4. (20 points) The waiting time, in hours, between successive speeders spotted by a radar unit is a continuous random variable with cumulative distribution -8x76 / le = 1- e 11-e dx x ZO; dv=e 0, f(x) = f'(X) = x < 0. 8 e V= 1 84 (a) Find the probability of waiting less than 10 minutes between successive speeders; hind the wyerane waiting time between successiye speeders spotted by a radar unit. 013-0il u=X -8X -81 -8% ge

數學/統計學/共變異數/相關係數 想請問一下題目上的第三題要如何求算ಥ_ಥ （網路上查到的題型都是實數對實數，這裡是給一個範圍⋯而且求的是開架跟天數而不是兩區的差別） 附上上課給的範例嗚嗚嗚 麻煩了ಥ_ಥ謝謝各位

Question 2 (125) V2 某家位於美國中部小鎮之小型房地產仲介,現想瞭解物件自委託到買賣成立所需的時間。該 公司分析近近三年來成交的 800 筆資料,整理如下表。 成交所需天數 30 天以內 31-90 天 90 天以上 總和 $150,000 以下 50 40 10 100 6 6:125 $150,000-$199,999 20 150 開價 80 250 0,3125 $200,000-$250,000 20 280 100 400 05 $250,000 以上 10 30 10 50 總和 100 500 200 800 如果該公司簽下委賣合約,開價在$150,000 以下,則成交天數在90 天以下的機率 為何? b. 如果事件 A表示成交所需天數在90天以上,事件B表示開價在$150,000 以下, 請問事件A與B 是否為獨立事件?試說明之。 C. 假設該公司將800 筆數據又細分為東區及西區(兩區房價分佈相似),並統計在售價 區間的平均銷售天數,其結果呈現如下表。試算共變異數及相關系數,說明開價與平 均銷售天數有甚麼關係。 平均銷售成所需天數 0,0625 a. 東區 西區 PC62 37 42 54 66 開價 $150,000 以下 $150,000-$199,999 $200,000-$250,000 $250,000 以上 71 82 46 50 出S(新) 法制度信天名之戈登发 才有哪 and AND cing 0 .action 2 (104)

感謝各位🙏

6@ The Agency for Healthcare Research and Quality reports that medical errors ae ITesponsible for injury to 1 out of every 25 hospital patients in the United States. (Data extracted from M. Ozan-Rafferty, “Hospitals: Never Havea Never Event,”The Gallup Management Journal。gmj. gallup.com, May 7, 2009.) These errors are tragic and &gxpensive.。Preventable health care-related errors cost an estimated $29 billion each year im the United States、Suppose that you Select a sample of 100 U.S- hospital patients- 結 What is the probability that the sample percentage reporting injury due to medieal grrors Will be between 5% and 10%? 也生he probability is 909% that the sample percentage will be within what symmetrieal Jimits ofthe population percentage? c he probability is 95% that the sample percentage will be within what symmetrical limits ofthe population percentage?

33題，有人可以幫我列算式就好嗎 是波氏分配（卜瓦松分配）題目

CHMAPTER 6 smen er replacem es, muff plecitlons w 1r 同 the numper oftransmissf sen0C7 polsson 昌關 dmwpute 4 o Shop. The! te dett Ave/lino's Aut 字 ee 3 stributlon le butlon ls the an summary, the Polsson dis 呈ty dlstob n summar OP 4 needed to construct a Poiss 4 on aa random variable, desl9! errors, or other r: ellhood t 的 elikeli nedthejkelJncoo 同 on nsurance Company ge 1 polic surar From actuary taples, Washington 2 gten nsurance aty 』 age 25 wi qie within the next year is pay ity they wi 25-year-ojg men this year' whatis the probabilty 3 JjnaPoisson distributionn 三0.4 a. What is the probapility thatx三0 b. What is the probability thatx > 0? 32. 全a Poisson distributionh 二4 a. What is the probapbility thatx 三 2? b. What js the probapbiljty thatx 生 2? f experience, c. What js the probability thatx> 2? m her years ol 還 officer at Coast Bank and Trust. Fro ble to repay 9 inot bea she estimates that the probability is .025 that an applicant wi hs or her jnstajiment loan. Last month she made 40 1 父 What js the probability that three loans will be 和 sfaulted? 紀 What js the probability that at least three loans will be del tthe rate oftwo per Automobijles arrive at the Elkhart exit ofthe Indiana Tol 同 ibution minute. Tne distribution of arrivals approximates a Poisson distri 了人 a.- What is fhe Probabifity that no automopbiles arrive in a particular uiar Pp. what js fhe Propabjlity that at least one automobile arrives during mrnute? 5 站5 estimated that 0.5% ofthe Callers to the Customer Service department of Dell Jnc. wil receive a busy signal. whatis the probability that oftoday's 1,200 callers at reast 5 received a Pbusy signal? 。 生如e past schools jn Los Angeles Couni year for weafher enmergencies. What is 1 Counfy wi close for 4 days next year? 24 ty have closed an average of 3 days each he probability that schools in Los Angeles opapjlity distribution js a !ting apjjty associated wjth each Out( discrete propapjjity distribution can aSsume only certain values. The main features are: _The sum offhes probabilties is 1.00. The probapijlity ofa particular outcome is between 0.00 and 1.00. Jheoutcomes are mutually exclusive. ontinuous djsfribution can assume an jmfnite number ofvalues within a speecsi iean and variance ofa probability distribution are Computed as follows, mean js equalto: Come- ific rang variance js egqual to: