ECMT2160: Computational 后端

【ECMT2160: Computational】ECMT2160: ComputationalAssignment
Due: November 3, 11:59am
This assessment task requires you to use MATLAB to run some Monte Carlo
simulations. You should prepare your submission as a MATLAB Live Script
file (i.e., a .mlx file). Submit your answers through the Canvas course website.
Your submission should include a mixture of written responses formatted as text,
blocks of MATLAB code, and MATLAB output, including graphs. You should
submit two versions of your answers: the original .mlx file, and a version ex-
ported to .html.
You may work on this assessment individually, or in pairs. If you work in
pairs, it is important that you clearly indicate the student ID number of your
partner in your submission. Your submission should not be identical to your
partner’s submission.
The assignment consists of two questions, each with multiple parts. Answer
all parts of both questions. The assignment is worth a total of 25 points towards
your final assessment. The first question is worth 15 points and the second ques-
tion is worth 10 points. Points will be deducted for poor presentation, including:
excessive typos, poor written expression, poor organization, etcetera.
1
Question 1
Before attempting Question 1, you should work through Sections 3.8 and 3.9 in
the file IntroProb.mlx. Begin your submitted solution to Question 1 by running
the command
rng(STUDENTID)
in MATLAB, where STUDENTID is your 9-digit Student ID number. This fixes
the sequence of random numbers to be generated in your simulation.
Suppose we roll two fair six sided dice. Let1 denote the sum of the numbers
rolled, and let 2 denote the maximum of the numbers rolled.
(a) (i) Create an 11 × 6 matrix containing the values taken by the joint prob-
ability mass function of 1 and 2. The entry in row , column of this
matrix should contain the probability P(1 = , 2 = ).
(ii) Create a three-dimensional bar graph displaying the joint probability
mass function of 1 and 2.
(b) (i) Create a 1× 6 vector containing the values taken by the marginal prob-
ability mass function of 2. The entry in column of this vector should
contain the probability P(2 = ).
(ii) Create a two-dimensional bar graph displaying themarginal probability
mass function of 2.
(c) (i) Create an 11 × 6 matrix containing the values taken by the conditional
probabilitymass function of1 given2. The entry in row , column of
this matrix should contain the conditional probability P(1 = |2 = ).
(ii) Create six two-dimensional bar graphs, each displaying the conditional
probability mass function of 1 given 2 = , with taking the values
1 through 6 in your six graphs.
2
(d) In each of 10,000 iterations of a “for loop”, do the following.
(i) Generate a discrete random variable whose probability mass function
is the marginal probability mass function of 2 calculated in part (b).
Hint: theMATLAB commandrandi(6,2,1) returns a 2×1 random
vector whose entries are independent random variables each equal to
the numbers 1 through 6 with equal probabilities.
(ii) Calculate the conditional expectation E(1 | 2 = ), where is the
random number generated in part (i).
Calculate the average of the conditional expectations computed over all 10,000
iterations of the “for loop”.
(e) Discuss how your findings in part (d) relate to the Law of Iterated Expecta-
tions.
3
Question 2
Let be a random variable with the standard normal distribution, and let() be
the probability density function of the standard normal distribution. Let (1, 2)
be the function
(1, 2) =
{
4(12)?4(?31 + ?32 ? 1)?7/3 if 0 < 1 < 1 and 0 < 2 < 1
0 otherwise.
Suppose that 1 and 2 are a pair of continuous random variables whose joint
probability density function is given by
(1, 2) = (P( ≤ 1), P( ≤ 2))(1)(2)
for all real 1 and 2.
(a) Create a graph of the joint probability density function of1 and2 for values
of 1 and 2 between ?3 and 3.
(b) Create a graph of the marginal probability density function of 1 for values
of 1 between ?3 and 3. Graph it alongside the standard normal probability
density function.
(c) Repeat part (b) for 2 instead of 1.
(d) Based on your answers above, do you think that the joint distribution of 1
and 2 is multivariate normal? Why or why not?

ECMT2160: Computational

推荐阅读

海门大桥

胃癌|胃癌偏爱这4类人，若你在其中，做好这5点，或许能幸免！

王者荣耀下载最新版安卓，王者荣耀助手安卓版下载

电商怎么做粮油电商是什么意思，粮油是啥

弈星重塑啦！从围棋的对弈体验入手，天才少年的成长的关键词是：以身入局，____ 王者荣耀8月5日每日一题答案

安卓强制前台,手机回收模式下安卓应用如何继续在后台运行?

电脑调哪几个设置可以让电脑变快速度电脑调哪几个设置可以让电脑变快

老款5角硬币图片「新款5元硬币」

西瓜汁放冰箱可以保存多久

qqbot源码分析,nginx源码分析

梦见抱着男孩

雨隐村曾经有几位首领火影忍者手游10月28日每日一题答案

你看过最好看的美剧是什么？

php长数据发送 php传输数据的方式

行政处罚的种类包括人身罚行为罚财产罚和申诫罚行政处罚的种类

mysql批量查询语句 mysql查询批量替换

六月黄吃到什么时候

小森生活游戏介绍小森生活好玩吗

鸡丸的做法大全鸡丸怎么做

秦时明月世界怎么转职秦时明月世界转职业