# 代写 MXB107 assignment Statistical Models for Data

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• 代写 MXB107 assignment Statistical Models for Data

MXB107 Semester 1 2016  Assignment 2 Question Sheet  Page 1 out of 2
Queensland University of Technology
ience and Engineering Faculty
School of Mathematical Sciences
MXB107 –  Statistical Models for Data: Relationship and Effects
Assignment #2 – Semester 1, 2016 – Question Sheet
Due: by 5:00pm on Friday 22nd April 2016.
on the 6th Floor of O-Block. Please ensure you attach a signed Official Assignment
Cover Sheet and include your tutorial time and tutor’s name.
Question 1 [4.5 marks]
Consider two continuous variables: X ~ Unif(0, 10), with f X (x) = 0.1, 0 ≤ x ≤ 10 and
Y ~ Exp(0.2), with f Y (y) = 0.2exp(–0.2y), y ≥ 0. Note that E(X) = E(Y) = 5.
a) Find Pr(X>a) and Pr(Y>a) for a = 5, 6, 8, 9.
b) Hence find Pr(X>a+1|X>a) for a = 5, 8. [Hint: The events A = (X>a+1)&(X>a) and
B = (X>a+1) are the same. (Can you see why?)] How do these probabilities compare
with Pr(X>1)?
c) Likewise, find Pr(Y>a+1|Y>a) for a = 5, 8 and compare with Pr(Y>1).
d) Comment briefly on how your results from parts (a) and (b) differ.
Question 2 [2.5 marks]
Let Z be a standard normal random variable and consider the equation
Pr{a < Z ≤ b} = 0.90.
a) If b = 2, find a. Similarly, if b = 2.5, find a.
b) Are there values of b for which the equation has no solution for a? If so, what are
they?
c) Consider all the values of b for which there is a corresponding value of a. What
choice of b do you think makes the range (a, b) shortest (i.e., makes b – a smallest)?
Question 3 [2 marks]
An established market research consultancy has decided to check its own market
profile. Out of a random sample of 100 local residents, they find that 42 have heard of
their brand name.
a) Based on this sample, construct a 99% confidence interval for the true proportion p
of local residents who have heard this brand name.
b) After constructing this interval, chief consultant feels that it is too wide to b useful and would like to shorten the interval; however, she does not want to chang the confidence level and decides instead to increase the sample size. Assuming the
observed proportion stays the same, how large a sample is needed to ensure an
interval with width of no more than 0.02?
MXB107 Semester 1 2016  Assignment 2 Question Sheet  Page 2 out of 2
Question 4 [3 marks]
Consider the following inspection scenarios:
(1) identify which of 50 nominally identical items have manufacturing defects, when it
has been established that 4% of items from this production line typically have defects;
(2) inspect 50km of copper wire for flaws, when flaws have been found to occur
randomly in this type of wire at an average rate of one flaw per 25km.
Let X be the number of defective items found in scenario (1) and Y be the number of
flaws found in scenario (2). Note that E(X) = E(Y) = 2.
a) Given that X ~ Bin(50, 0.04), calculate Pr(X=0), Pr(X=1) and Pr(X>1).
b) State a realistic distribution for Y and calculate Pr(Y=0), Pr(Y=1) and Pr(Y>1).
c) Now consider another variable Z ~ Bin(500, 0.004). Based on your findings from (a)
and (b), estimate Pr(Z=0), Pr(Z=1) and Pr(Z>1) to 3 decimal places.
Question 5 [3 marks]
[Note: the context of this question was framed by last semester’s lecturer, Prof. Steve
Stern, but I liked it so much that I have only changed the numbers.] Believe it or not,
while writing this assignment, I traveled forward in time and collected a random sampl of 25 submissions for this assignment. The names on the assignments did not survive
the return time-trip, but I could still calculate the average total score on the sampled
assignments, which was 10, and their sample standard deviation, which was 1.8. On the
basis of this information:
a) Find a 95% confidence interval for the actual average score μ for the entire class.
b) Construct a 99/95 tolerance interval for your score on this assignment (i.e., an
interval that includes 99% of possible observations with 95% confidence). Discuss
any issues.

代写 MXB107 assignment Statistical Models for Data
c) While collecting the sample, I met my future self, who told me the actual mean and
standard deviation of scores for all submitted assignments. Unfortunately, the
time-travel sickness I experienced on my return trip to the present meant I wa only able to remember the standard deviation, which was 2.0. Given this
information, how would you change the interval you calculated in part (a), if at all?

代写 MXB107 assignment Statistical Models for Data