Homework answers / question archive / Sunway University  MAT1034 / Assignment (Q) / AUG 2020 BAS/BinDS/BFA/BFE 2 Question 1 (10 Marks) a) Create a “random sphere” whose radius, r, is determined by the distribution table given below

Sunway University  MAT1034 / Assignment (Q) / AUG 2020 BAS/BinDS/BFA/BFE 2 Question 1 (10 Marks) a) Create a “random sphere” whose radius, r, is determined by the distribution table given below

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MAT1034 / Assignment (Q) / AUG 2020
BAS/BinDS/BFA/BFE
2
Question 1 (10 Marks)
a) Create a “random sphere” whose radius, r, is determined by the distribution table given
below.
Radius, r 1 2 3 4 5 6
( )
P r 0.25 0.1 0.3 0.2 0.10 0.05
Let V be the volume of the sphere. Find [ ]
E V . Show all your calculation.
b) Using R, generate n radius values based on the assigned probabilities to obtain volume for
n spheres. Complete the table below.
n [ ]
E V
10
100
1000
c) Compare and discuss the answers in part (a) and (b).
Description Mark allocation
a) Calculation 2
b) R code.
Outcomes
5
c) Discussion 3

Question 2 (10 Marks)
a) Provide the list of variables and the description for the dataset you have selected in the
table below:
Variable Description
b) Identify a continuous random variable from the dataset you have chosen. Using R, apply
summary() function on the continuous random variable that you have chosen from the
dataset. Discuss the values of the summary and comment on the distribution of the data.
c) Using R, calculate the standard deviation for this continuous random variable.
d) Using R, create a histogram with all appropriate labels for the variable you have chosen in
part (b).
e) Let Y be a random variable that you have chosen in part (b). Using Chebyshev's Theorem,
find the value of C such that ( ) 0.25
P Y C
?
− ? ? . Interpret your answer.
Description Mark allocation
a) Variable description 1
b) R code.
Discussion
2
c) Standard Deviation 1
d) Histogram with appropriate labels and
limit
2
e) Calculation
Interpretation
4
Select one dataset from the Question 2 folder that is available on eLearn. In your report, specify the dataset name and description. Data description can be obtained from https://rdrr.io/cran/Stat2Data/man/AccordPrice.html. Attach the first 10 records of your dataset in appendix.

Question 3 (5 Marks)
A multinational company offers a health insurance policy to its employees in Malaysia. This
policy offers additional coverages for mental illness, stroke and cancer. The Question3.csv file
contains the dataset of 500 employees and their choices of the additional coverages. Using R,
find the probability that a randomly chosen staff will opt for none of the additional coverages.
Question 4 (5 Marks)
A survey was conducted among 60 undergraduate students on the number of times they had
attended the school's tutoring session in the last week. The results are shown below:
Study Mode
Number of Times
1 2 3
Full Time 12 25 8
Part Time 2 5 8
a) What is the probability the student visited the tutoring session two times, given that the
student is full time?
b) Verify the answer by simulating this in R for 10000
n = . Provide explanation for each line
of your code.
Description Mark allocation
a) Calculation 1
b) Codes and explanation 4