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問題的種類

數學與統計 大學

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

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數學 高中

根本看不懂啦\( ̄▽ ̄;)/

Your report should follow these guidelines, although you may choose how you present it: How to Write a Mathematics Report In writing your report, remember that you are writing up a mathematical story and so, like all good stories, it will need a beginning, a middle and an end. More formally, the main components of this writing style are: Introduction, Formulating the Problem, Solving the problem, Discussion of Results, and Conclusion. We will now consider some of the detail in each of these aspects. Introduction This is the beginning of the story. Give a brief explanation of what the problem is about what the goals of the report are and what will be presented. Assume that your reader does not know what the problem is about or how to solve it. Formulating the problem Translate the situation into a maths problem. Explain how you will begin to solve the problem and break it into simpler stages. Discuss any assumptions made. What quantities are variables and which values are fixed? You may use sub-headings if they assist you. Solving the Problem Show any calculations and mathematical reasoning that you use. (Assume that your reader does not know much maths). Do not show the same types of calculations repetitively. Just give one or two examples of a calculation and then put the rest of the results in a table. Use diagrams or graphs if they assist you. Make general remarks about what you observe in your calculation results and, possibly, why. You may want to criticise your work and go on to improve it in the next section. Explain what you will do next and why. Discussion of Results - Evaluate and Verify Summarise your results if necessary and refer to your mathematical reasoning. Justify procedures used. Interpret your results. First, are they reasonable or does something not look right and need further investigation or checking? Is there a decision to be made? Here is where you should present the decision-making process. Evaluate the strengths and limitations of your solutions. Conclusion Summarise your findings. Refer to the problem outlined in the introduction. Make sure that you answer the question that was asked. Make recommendations. No new material should be presented here.

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