代做Quantitative Methods Semester 1, 2024 midterm exam代写Java编程

日期：2024-08-28 06:36

Quantitative Methods (M)

Semester 1, 2024

Sample midterm exam

Question 1 (10 marks)

The following data set contains the end-of-month ordinary stock price of Google’s parent company, Alphabet Inc., for each month over the period from May 2023 to March 2024 (rounded to the nearest USD):

142

136

130

115

118

131

128

126

124

114

119

a.   Calculate the mean and standard deviation for the sample of stock prices. (2 marks)

b.   Calculate the five number summary for the sample of stock prices. (2 marks)

c.   Calculate lower and upper fences for the sample of stock prices. (2 marks)

d.   Using your answers above and/ or otherwise, draw a box-plot for the sample of stock prices. Hint: Ensure that your box-plot is in line with best principles for the visual presentation of statistical information. (4 marks)

Question 2 (10 Marks)

A roulette wheel has 37 numbers in total (ranging from 0 to 36) and the following properties:

●    18 red, 18 black and 1 green number

●    18 odd and 18 even numbers

●    12 low, 12 mid-range and 12 high numbers

●    A left column (C1) for the numbers 1, 4, 7, …, 34

●    A middle column (C2) for the numbers 2, 5, 8, …, 35

● A right column (C3) for the numbers 3, 6, 9, …, 36

The graphic to the right demonstrates the relationships between all of the properties discussed above.

‘Red’ numbers are circled and ‘Black’ numbers are circled and filled with black.

The ‘Green’ number (zero) is neither circled nor circled and filled in black. It is separate from all other categories – it is not black nor is it red, not even/odd, not low/mid-range/high, not left/middle/right. It is by itself.

a.   What is the probability of a low C3 number coming up on a single turn? (1 mark)

b.   What is the probability of seeing high numbers on 3 consecutive turns? (2 marks)

c.   What is the conditional probability of an even number coming up on a single turn given that you know that the number which came up is amid-range black number? (2 marks)

d.   Let event ‘E ’ be a roulette spin which lands on an even number, event ‘L’ be a roulette spin which lands on a low number, and event ‘B’ be a roulette spin which lands on a black number. Also, let event ‘Z’ be a roulette spin which lands on the number zero, where the marginal probability of Z is P(Z) = 0.027.

i)         Which number on the roulette wheel makes the following statement true: P(E′ ∩ L ∩ B) ≠ 0 ? (1 mark)

ii)        True or False: Z ∩ E′ ∩ L ∩ B = φ. Hint: Mutually exclusive. (1 mark)

iii)       Use the conditional probability P(Z  │ E ′ ∩ L ∩ B) to show that event Z is not independent of event E′ ∩ L ∩ B. (3 marks)

Question 3 (10 Marks)

You are a graduate auditor at EY and you’ve been asked by your manager to verify the accuracy of 4 invoices issued by a client firm which EY is auditing. Your manager informs you that, based on prior year audits, the probability of an invoice being accurate is 60%.

a.   Which method for assigning probabilities has your manager used in his estimation? (1 mark)

b.   What is the probability that exactly 1 of the 4 sampled invoices is accurate? (1 mark)

c.   State one assumption which underlies your calculation in part (b). Hint: There are several to choose from. (1 mark)

d.   What is the probability that at least two of the sampled invoices are accurate? (3 marks)

e.   Using the probabilities calculated above and/ or otherwise,  graph the PDF which applies to your sample of invoices. Hint: Ensure that your PDF is complete and is in line with best principles for the visual presentation of statistical information. (4 marks)

Question 4 (10 Marks)

The estimator produces individual estimates for μ the mean of a population. Use this information to answer the following questions:

a.   Assuming you’re sampling without replacement, how many sample means does the sampling distribution of contain if n = 20 and N = 35? (2 marks)

b.   Assuming you’re sampling with replacement, how many samples of size n = 10 does the sampling distribution of contain if there are 23 observations in the population? (1 mark)

c.   State the mathematical rule which describes the statistical bias of . (1 mark)

d.   Is a consistent estimator? Explain why or why not. (2 marks)

e. is the MVUE for μ. Carefully explain what this means. (2 marks)

f.   Calculate the standard error of the sampling distribution.