一站式論文代寫,英国、美国、澳洲留学生Essay代寫—FreePass代写

程序代寫案例-FP0060
時間:2021-06-13
FP0060
1 (Continued)
UNIVERSITY OF WARWICK
File-based Open Book Assessment (2 hours)
Warwick Foundation Studies
FP0060 STATISTICS AND FURTHER MATHEMATICS
Student Instructions:

1. Read these instructions fully and before you start the assessment.
Read through the paper at least once before you start writing

2. There are 10 questions. Candidates should attempt every question.

3. You should not submit answers to more than the required number of questions.

4. The maximum mark for this paper is 100.

5. Answers must be handwritten, either on paper or using an electronic tablet, and
uploaded to the AEP within a single PDF file.

6. You should write legibly, preferably in dark blue or black ink. If you use a pencil
ensure that it is not too faint to be captured by a scan or photograph.

7. When uploading photographs or scans of your work please check for legibility
before uploading. It is your responsibility to ensure that your work can be read.

8. Start each question on a new page, and only write on one side of each piece of
paper. Label each question (number and part) clearly.

9. Write your student ID number in the top corner of each page (but not your name).

10. You are allowed to access module materials, notes and resources on Moodle
during the assessment. You must not use any other websites or resources.

11. You may use a scientific calculator and the formula book provided to help you
answer the questions.

12. You must not communicate with any other candidate during the assessment
period.

You may be contacted for a video call to discuss some of your answers. You should
therefore keep the original copy of your work and be available via email/Teams in
case you are contacted.

13. By starting this assessment you are declaring yourself fit to undertake it. You are
expected to make a reasonable attempt at the assessment by answering the
questions in the paper.

14. You have 2 hours to complete the assessment. You should upload your
assignment to the AEP within the required timeframe (see below).
FP0060
2 (Continued)
Please note that:

- We strongly recommend you use Google Chrome or Mozilla Firefox to access
the Alternative Exams Portal.

- You must have completed and uploaded the assessment within the fixed time
available.

- You have an additional 45 minutes beyond the stated duration of this
assessment to allow for downloading and uploading the assessment, your files,
and technical delays. This time should not be used to continue writing your
answers.

- Late submissions are not accepted. Once started, you must complete the
assessment within 2 hours and then upload your files within 45 minutes.

- If you are unable to submit your assessment, you can record Mitigating
Circumstances. Your case will be considered and you will be notified of the
outcome.

- If you have pre-approved Alternative Exam Arrangements (Reasonable
Adjustments) that permit extra time and/or rest breaks this time will be added on
to the stated duration.






























FP0060
3 (Continued)
Support During the Assessment

Operational Support

Use the AEP to seek advice immediately if during the assessment period:

? you cannot access the online assessment;
? you believe you have been given access to the wrong online assessment;

Notify the invigilator (using the ‘Contact an Invigilator’ tool in the AEP) if you
have an academic query about the assessment.

Operational support will be available between 09:00 and 17:00 (UK Time).


Technical Support

? If you experience any technical difficulties with the Alternative Exam Portal
please contact helpdesk@warwick.ac.uk

? If you experience technical difficulties with Moodle please contact
moodle@warwick.ac.uk

Technical support will be available between 09:00 and 17:00 GMT (UK Time).


Academic Support

If you have an academic query, contact the invigilator (using the ‘Contact an Invigilator’
tool in AEP) to raise your issue. Please be aware that two-way communication in AEP
is not currently possible.

Academic support will be provided for the duration of the full examination period
(i.e. 2 hours (+45 min)). Academic support beyond this time is at the discretion of the
department.


Other Support

Write to your module convenor/department immediately if you cannot complete
your assessment for the following reasons:

? you lose your internet connection;
? your device fails;
? you become unwell and are unable to continue;
? you are affected by circumstances beyond your control (e.g. fire alarm).



Your assessment starts below.
FP0060
1. The events A and B are independent with P (A) =
1
6
and P (A ∪B) = 4
9
.
(a) Find P (B).
Give your answer as a fraction. (3 marks)
(b) Draw a Venn diagram to illustrate the events A and B and the probabilities
for each region. (3 marks)
(c) Find P ((A′ ∩B) ∪ (A ∩B′)).
Give your answer as a fraction. (2 marks)
(d) Find P (B′ |A).
Give your answer as a fraction. (2 marks)
2. The probability distribution of the discrete random variable X is given by:
x 1 3 5
P (X = x) 0.2? a 2a 0.8? a
where a is a constant.
(a) State the range of possible values of a. (2 marks)
(b) Show that E(X) is independent of a. (2 marks)
(c) Given that Var(X) = 1.6, calculate the value of a. (3 marks)
Two independent observations of X, denoted X1 and X2, are considered.
(d) Calculate P (X1 +X2 = 6).
Give your answer as a fraction. (3 marks)
4 (Continued)
FP0060
3. The length of time, in minutes, that patients spend waiting at a doctor’s surgery is modelled by
the continuous random variable, T , with the following cumulative distribution function:
F (t) =
???????
0 t < 0
1
56000
(?t3 + 45t2 + 1200t) 0 ≤ t ≤ 40
1 t > 40
(a) Find the probability that a patient has to wait more than 20 minutes.
Give your answer as a fraction. (3 marks)
(b) Define fully the probability density function f(t) of T . (3 marks)
(c) Find the modal waiting time in minutes of a patient at the doctor’s surgery. (3 marks)
(d) Give one reason why this model may need to be refined. (1 mark)
4. A manufacturing company produces batteries.
The probability that a battery is faulty is 0.25.
A random sample of 10 batteries is selected.
(a) Write down a suitable distribution to model the number of faulty batteries
in the sample. (1 mark)
(b) Write down two assumptions you have made for your model in part (a). (2 marks)
(c) Find the probability that there is exactly 2 faulty batteries in the sample.
Give your answer to four decimal places. (2 marks)
(d) Find the probability that there are at least 3 faulty batteries in the sample.
Give your answer to four decimal places. (2 marks)
The batteries are sold in multipacks of 10. A customer buys 4 multipacks.
(e) Find the probability that exactly 2 of these multipacks contain at least 3 faulty
batteries. Give your answer to four decimal places. (3 marks)
5 (Continued)
FP0060
5. In a population, 10% of the people are left-handed.
A random sample of 50 people is taken from this population.
(a) Using a suitable Binomial distribution, calculate the probability that in this sample
there are more than 10 people in the sample who are left-handed.
Give your answer to four decimal places. (2 marks)
A second random sample of 400 people is taken from the population.
(b) Using a suitable Normal approximation, estimate the probability that in this sample
there are between 30 and 50 (inclusive) people who are left-handed.
Give your answer to four decimal places. (8 marks)
6. Use the method of Lagrange Multipliers to optimise the function
f(x, y, z) = x+ y + z
subject to the constraint
g(x, y, z) = x2 + y2 + z2 = 3
(10 marks)
7. The plane Π1 has vector equation: r ·
?? 2-5
1
?? = 4
(a) Find the perpendicular distance from the point (7, 3, 13) to the plane Π1. (2 marks)
The plane Π2 passes through the point (-2, -3, 2) and is perpendicular to the vector
?? 31
-1
??.
(b) Show that the Cartesian equation of Π2 is 3x+ y ? z = ?11. (2 marks)
(c) Show that Π1 and Π2 are perpendicular. (2 marks)
(d) Find an equation for the line of intersection of Π1 and Π2.
Give your answer in the form r = a + tb, where a and b are constant vectors
and t is a scalar parameter. (4 marks)
6 (Continued)
FP0060
8. The matrix A is given by
A =
??1 0 20 1 -1
0 0 2
??
(a) Calculate the determinant of A. (2 marks)
The plane Π1 has vector equation:
r =
?? 2-2
4
??+ λ
??10
1
??+ μ
??-22
1
??
The plane Π1 is transformed to the plane Π2 by the transformation matrix represented by the
matrix A.
(b) Find an equation of the plane Π2 in the form r · n = ρ. (8 marks)
9. Find in the form y = f(x) the general solution of the differential equation
d2y
dx2
? 3dy
dx
+ 2y = 4x2
(10 marks)
10. (a) Show that the substitution z =
1
y3
transforms the first order differential equation
dy
dx
+
y
x
= ?2y4, x > 0, y > 0 (?)
into the linear first order differential equation
dz
dx
? 3
x
z = 6 (??)
(3 marks)
(b) Find the general solution of the differential equation (??). (5 marks)
(c) Hence, find the general solution of the differential equation (?).
Give your answer in the form y3 = f(x). (1 mark)
Given that y = 1 at x = 1.
(d) Find the particular solution of the differential equation (?). (1 mark)
7 (End)

學霸聯盟

在線客服

售前咨詢
售后咨詢
微信號
Essay_Cheery
微信
专业essay代写|留学生论文,作业,网课,考试|代做功課服務-PROESSAY HKG 专业留学Essay|Assignment代写|毕业论文代写-rushmyessay,绝对靠谱负责 代写essay,代写assignment,「立减5%」网课代修-Australiaway 代写essay,代写assignment,代写PAPER,留学生论文代写网 毕业论文代写,代写paper,北美CS代写-编程代码,代写金融-第一代写网 作业代写:CS代写|代写论文|统计,数学,物理代写-天天论文网 提供高质量的essay代写,Paper代写,留学作业代写-天才代写 全优代写 - 北美Essay代写,Report代写,留学生论文代写作业代写 北美顶级代写|加拿大美国论文作业代写服务-最靠谱价格低-CoursePass 论文代写等留学生作业代做服务,北美网课代修领导者AssignmentBack