n insurance portfolio consists of two homogeneous groups of clients; N i, (i = 1 , 2) denotes the number of claims occurred in the ith group in a fixed time period. Assume that the r.v.'s N 1, N 2 are independent and have Poisson distributions, with expected values 200 and 300, respectively.

The amount of an individual claim in the first group is a r.v. equal to either 10 or 20 with respective probabilities 0.3 and 0.7, while the amount of an individual claim in the second group equals 20 or 30 with respective probabilities 0.1 and 0.9.

Let N be the total number of claims, and let S be the total aggregate claim.

Find E { S } and V a r { S }.

(Hint: Compute E { Y i } and E { Y i 2 } proceeding from the result of Question 10 and use Propositions 1-2 that we proved in class regarding E { S } and V a r { S } in the case where N is a Poisson r.v.)

8. A professor tests whether the loudness of noise during an exam (low, medium, and high) is independent of exam grades (pass, fail). The following table shows the observed frequencies for this test.

Part A) Conduct a chi-square test for independence at a 0.05 level of significance. (Round your answer to two decimal places.)

Decide whether to retain or reject the null hypothesis.

Part B) Compute effect size using Cramer's V. (Round your answer to two decimal places.)

9. What is Cramer's V for each of the following values for the chi-square test for independence? (Round your answers to two decimal places.)

Part A) X² = 3.63, n = 50, df_smaller = 1

Part B) X² = 9.27, n = 120, df_smaller = 2

Part C) X² = 12.23, n = 160, df_smaller = 3

Use the following assumptions for this question. The commercial banking system has a target reserve ratio of 5% and there is no cash drain. A new immigrant to the country makes a cash deposit of $1,000. In the following table show how deposits, reserves, and loans change as the new deposit permits the banks to “create” money.

1. A) Complete the entire table.
2. B) You have now completed the first five rounds of the deposit-creation process. What is the total change in deposits so far as a result of the single new deposit of $1000?
3. C) This deposit-creation process will go on forever, but it will have a finite sum. In the text, we showed that the eventual total change in deposits is equal to 1/v times the new deposit, where v is the target reserve ratio. What is the eventual total change in deposits in this case?
4. D) What is the eventual total change in reserves? What is the eventual change in loans?

The working gas of a thermodynamic cycle is air(assume constant specific heats.)The gas originally starts at 100kPa, 4m3and 27oC. It undergoes a four step process:Process A-B: The gas is compressed at constant temperature to one-fourth of its volume. Process B-C: The volume of the gas is then doubled at constant pressure. Process C-D:The gas then undergoes an adiabatic expansion.Process D-A:The gas then undergoes a constant volume process back to its original statea) Make a table of the temperature, pressure, volume, internal energy, enthalpy, entropy and quality factor (T, P, V, U, H, S & x) at the start of each process.b) Make a table of the change in internal energy, heat flow, work done, change in enthalpy, and change in entropy (U, Q, W, H, S) during each leg of the cycle.c) Draw a well-labelled P-v diagram (indicating lines of constant temperature.)d) Calculate the thermal efficiency of the cycle.

1. An ideal transformer has a primary with 25 turns and secondary with 15 turns. The load resistor is 24 ? and the source voltage is 85 Vrms.What is the rms electric potential across the 24 ? load resistor?

Answer in units of Vrms

2. A transformer consists of two coils of wire wound on a common toroidal iron core. The mutual inductance of the pair is 483 mH and the current in the first coil decreases from 29 A to 0 in 2.9 s.

What is the induced emf in the second coil? Answer in units of V.

3.If the outer coil has 14.7 turns, a radius of 19 cm and length of 7.47 cm and the inner coil has 628 turns, a radius of 7 cm, and a length of 33.3 cm, find the mutual inductance of the circular coil and solenoid.

Answer in units of ?H

4. Now the current in the solenoid is increased linearly at a rate of di/dt = a =20.2 A/s.

What is the magnitude of the voltage E across the circular coil?

Answer in units of ?V.

Your friend’s professor gives out reasonably hard exams 70% of the time, and ridicu- lously hard exams 30% of the time. On hard exams, each student’s score on the exam is a normally distributed random variable with μH = 70 and σH = 10. On ridiculously hard exams, each student’s score on the exam is a normally distributed random variable with μR = 50 and σR = 15. Suppose you have four friends in the class, not just one. Let A be the average score of your four friends: A= (F1 +F2 +F3 +F4)/ 4 Where F1 is your first friend’s score, and F2 is your second friend’s score. Find E[A] and V ar(A) if the exam is ridiculously hard. (e) Find E[A] and V ar(A) if the exam is reasonably hard. (f) Since A is the sum of normal random variables, it is itself a normal random variable. Find P (A > 65) if the exam is reasonably hard, and if it is ridiculously hard. (g) If A is greater than 65, what is the probability the exam was ridiculously hard?

Suppose a small cannonball weighing 20 pounds is shot vertically upward, with an initial velocity v0 = 340 ft/s. The answer to the question "How high does the cannonball go?" depends on whether we take air resistance into account. If air resistance is ignored and the positive direction is upward, then a model for the state of the cannonball is given by d2s/dt2 = −g (equation (12) of Section 1.3). Since ds/dt = v(t) the last differential equation is the same as dv/dt = −g, where we take g = 32 ft/s2. If air resistance is incorporated into the model, it stands to reason that the maximum height attained by the cannonball must be less than if air resistance is ignored. (a) Assume air resistance is proportional to instantaneous velocity. If the positive direction is upward, a model for the state of the cannonball is given by m dv dt = −mg − kv, where m is the mass of the cannonball and k > 0 is a constant of proportionality. Suppose k = 0.0025 and find the velocity v(t) of the cannonball at time t.

13)) a) Consider the following half-reactions: Half-reaction E° (V) F2(g) + 2e- 2F-(aq) 2.870V 2H+(aq) + 2e- H2(g) 0.000V Zn2+(aq) + 2e- Zn(s) -0.763V

(1) The weakest oxidizing agent is: enter formula

(2) The strongest reducing agent is:

(3) The strongest oxidizing agent is:

(4) The weakest reducing agent is:

(5) Will F-(aq) reduce Zn2+(aq) to Zn(s)?

(6) Which species can be reduced by H2(g)? If none, leave box blank.

b))

Consider the following half-reactions: Half-reaction E° (V) Ag+(aq) + e- Ag(s) 0.799V Co2+(aq) + 2e- Co(s) -0.280V Fe2+(aq) + 2e- Fe(s) -0.440V

(1) The weakest oxidizing agent is: enter formula

(2) The strongest reducing agent is:

(3) The strongest oxidizing agent is:

(4) The weakest reducing agent is:

(5) Will Ag(s) reduce Fe2+(aq) to Fe(s)?

(6) Which species can be oxidized by Co2+(aq)? If none, leave box blank.

c))

Consider the following half-reactions: Half-reaction E° (V) I2(s) + 2e- 2I-(aq) 0.535V Co2+(aq) + 2e- Co(s) -0.280V Cr3+(aq) + 3e- Cr(s) -0.740V

(1) The strongest oxidizing agent is: enter formula

(2) The weakest oxidizing agent is:

(3) The weakest reducing agent is:

(4) The strongest reducing agent is:

(5) Will Cr3+(aq) oxidize I-(aq) to I2(s)?

(6) Which species can be oxidized by Co2+(aq)? If none, leave box blank.

Question 3 (5 + 5 + 4 = 14 Marks)
a. Match FIVE of the 11 audit sampling terms (1-11) with the five definitions
provided below in items (i-v):
1. attributes sampling
2. block sample selection
3. haphazard sample selection
4. non-statistical sampling
5. probability proportional to size
6. random selection
7. representative sample
8. sampling distribution
9. statistical sampling
10. stratified sampling
11. systematic sample selection
i the use of mathematical measurement techniques to calculate formal
statistical results and quantify sampling risk.
ii a statistical, probabilistic method of sample evaluation that results in an
estimate of the proportion of items in a population containing a characteristic
of interest.
iii a non-probabilistic method of sample selection in which items are chosen
without regard to their size, source, or other distinguishing characteristics.
iv a method of sampling in which all the elements in the total population are
divided into two or more subpopulations that are independently tested and
statistically measured.
v a sample in which every possible combination of items in the population has
an equal chance of constituting the sample.
Required:
State the above individual definition (i to v) is defined as which audit sampling item?

Suggested Answer for part a:
Click or tap here to enter text.

b. Describe the audit risk model and the interrelationships of its components. Which
components of the audit risk model can be controlled by the auditor?
Suggested Answer for part b:
Click or tap here to enter text.

BUACC5935 Auditing and Assurance Services Semester 2 2020

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c. Outline the difference between tests of control and substantive tests and give an
example of a substantive test.