The total weekly cost of fringe benefits of dynamo productions. They employ 250 workers with gross payroll of $ 123 , 400 per week with fringe benefits are 5 % of gross payroll for sick days and holiday leave 8 % for health insurance and $ 12.40 per employee for dental insurance.

Question

Module Code: MATH380202 3. (a) Let {} be a white noise process with variance σ2. Define an ARMA(p,q) process {X} in terms of {+} and state (without proof) conditions for {X} to be (i) weakly stationary and (ii) invertible. Define what is meant by an ARIMA (p, d, q) process. Let {Y} be such an ARIMA(p, d, q) process and show how it can also be represented as an ARMA process, giving the AR and MA orders of this representation. (b) The following tables show the first nine sample autocorrelations and partial auto- correlations of X and Y₁ = VX+ for a series of n = 1095 observations. (Notice that the notation in this part has no relationship with the notation in part (a) of this question.) Identify a model for this time series and obtain preliminary estimates for the pa- rameters of your model. X₁ = 15.51, s² = 317.43. k 1 2 3 4 5 6 7 Pk 0.981 0.974 0.968 akk 0.981 0.327 8 9 0.927 0.963 0.957 0.951 0.943 0.935 0.121 0.104 0.000 0.014 -0.067 -0.068 -0.012 Y₁ = VX : y = 0.03, s² = 11.48. k 1…

Answer 1

Question

Chapter 9.III, Problem 16TIE

(a)

To determine

To calculate: The total weekly cost of fringe benefits of dynamo productions. They employ 250

workers with gross payroll of $123,400 per week with fringe benefits are 5% of gross payroll

for sick days and holiday leave 8% for health insurance and $12.40 per employee for dental

insurance.

(b)

To determine

To calculate: The percentage of payroll $123,400 the fringe benefit $19,142 represent.

(c)

To determine

To calculate: The cost of fringe benefit $19,142 for one year.

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Module Code: MATH380202 3. (a) Let {} be a white noise process with variance σ2. Define an ARMA(p,q) process {X} in terms of {+} and state (without proof) conditions for {X} to be (i) weakly stationary and (ii) invertible. Define what is meant by an ARIMA (p, d, q) process. Let {Y} be such an ARIMA(p, d, q) process and show how it can also be represented as an ARMA process, giving the AR and MA orders of this representation. (b) The following tables show the first nine sample autocorrelations and partial auto- correlations of X and Y₁ = VX+ for a series of n = 1095 observations. (Notice that the notation in this part has no relationship with the notation in part (a) of this question.) Identify a model for this time series and obtain preliminary estimates for the pa- rameters of your model. X₁ = 15.51, s² = 317.43. k 1 2 3 4 5 6 7 Pk 0.981 0.974 0.968 akk 0.981 0.327 8 9 0.927 0.963 0.957 0.951 0.943 0.935 0.121 0.104 0.000 0.014 -0.067 -0.068 -0.012 Y₁ = VX : y = 0.03, s² = 11.48. k 1…

Let G be a graph with n ≥ 2 vertices x1, x2, . . . , xn, and let A be the adjacency matrixof G. Prove that if G is connected, then every entry in the matrix A^n−1 + A^nis positive.

Module Code: MATH380202 1. (a) Define the terms "strongly stationary" and "weakly stationary". Let {X} be a stochastic process defined for all t € Z. Assuming that {X+} is weakly stationary, define the autocorrelation function (acf) Pk, for lag k. What conditions must a process {X+) satisfy for it to be white noise? (b) Let N(0, 1) for t€ Z, with the {+} being mutually independent. Which of the following processes {X+} are weakly stationary for t> 0? Briefly justify your answers. i. Xt for all > 0. ii. Xo~N(0,) and X₁ = 2X+-1+ &t for t > 0. (c) Provide an expression for estimating the autocovariance function for a sample X1,..., X believed to be from a weakly stationary process. How is the autocor- relation function Pk then estimated, and a correlogram (or acf plot) constructed? (d) Consider the weakly stationary stochastic process ✗+ = + + +-1+ +-2 where {E} is a white noise process with variance 1. Compute the population autocorre- lation function Pk for all k = 0, 1, ....

Answer 2

Question

Chapter 9.III, Problem 16TIE

(a)

To determine

To calculate: The total weekly cost of fringe benefits of dynamo productions. They employ 250

workers with gross payroll of $123,400 per week with fringe benefits are 5% of gross payroll

for sick days and holiday leave 8% for health insurance and $12.40 per employee for dental

insurance.

(b)

To determine

To calculate: The percentage of payroll $123,400 the fringe benefit $19,142 represent.

(c)

To determine

To calculate: The cost of fringe benefit $19,142 for one year.

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Answer 3

Question

Chapter 9.III, Problem 16TIE

(a)

To determine

To calculate: The total weekly cost of fringe benefits of dynamo productions. They employ 250

workers with gross payroll of $123,400 per week with fringe benefits are 5% of gross payroll

for sick days and holiday leave 8% for health insurance and $12.40 per employee for dental

insurance.

(b)

To determine

To calculate: The percentage of payroll $123,400 the fringe benefit $19,142 represent.

(c)

To determine

To calculate: The cost of fringe benefit $19,142 for one year.

Expert Solution & Answer

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Answer 4

Question

Chapter 9.III, Problem 16TIE

(a)

To determine

To calculate: The total weekly cost of fringe benefits of dynamo productions. They employ 250

workers with gross payroll of $123,400 per week with fringe benefits are 5% of gross payroll

for sick days and holiday leave 8% for health insurance and $12.40 per employee for dental

insurance.

(b)

To determine

To calculate: The percentage of payroll $123,400 the fringe benefit $19,142 represent.

(c)

To determine

To calculate: The cost of fringe benefit $19,142 for one year.

Expert Solution & Answer

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Answer 5

Chapter 9.III, Problem 16TIE

(a)

To determine

To calculate: The total weekly cost of fringe benefits of dynamo productions. They employ 250

workers with gross payroll of $123,400 per week with fringe benefits are 5% of gross payroll

for sick days and holiday leave 8% for health insurance and $12.40 per employee for dental

insurance.

(b)

To determine

To calculate: The percentage of payroll $123,400 the fringe benefit $19,142 represent.

(c)

To determine

To calculate: The cost of fringe benefit $19,142 for one year.

Answer 6

Chapter 9.III, Problem 16TIE

(a)

To determine

To calculate: The total weekly cost of fringe benefits of dynamo productions. They employ 250

workers with gross payroll of $123,400 per week with fringe benefits are 5% of gross payroll

for sick days and holiday leave 8% for health insurance and $12.40 per employee for dental

insurance.

Answer 7

Chapter 9.III, Problem 16TIE

(a)

To determine

To calculate: The total weekly cost of fringe benefits of dynamo productions. They employ 250

workers with gross payroll of $123,400 per week with fringe benefits are 5% of gross payroll

for sick days and holiday leave 8% for health insurance and $12.40 per employee for dental

insurance.

Answer 8

(b)

To determine

To calculate: The percentage of payroll $123,400 the fringe benefit $19,142 represent.

Answer 9

(b)

To determine

To calculate: The percentage of payroll $123,400 the fringe benefit $19,142 represent.

Answer 10

(c)

To determine

To calculate: The cost of fringe benefit $19,142 for one year.

Answer 11

(c)

To determine

To calculate: The cost of fringe benefit $19,142 for one year.

Answer 12

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Answer 23

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The total weekly cost of fringe benefits of dynamo productions. They employ 250 workers with gross payroll of $ 123 , 400 per week with fringe benefits are 5 % of gross payroll for sick days and holiday leave 8 % for health insurance and $ 12.40 per employee for dental insurance.

Solution Summary: The author calculates the total weekly cost of fringe benefits of dynamo productions.

Concept explainers

Videos

To calculate: The total weekly cost of fringe benefits of dynamo productions. They employ 250

workers with gross payroll of $123,400 per week with fringe benefits are 5% of gross payroll

for sick days and holiday leave 8% for health insurance and $12.40 per employee for dental

insurance.

To calculate: The percentage of payroll $123,400 the fringe benefit $19,142 represent.

To calculate: The cost of fringe benefit $19,142 for one year.

Chapter 9 Solutions

The total weekly cost of fringe benefits of dynamo productions. They employ 250 workers with gross payroll of $ 123 , 400 per week with fringe benefits are 5 % of gross payroll for sick days and holiday leave 8 % for health insurance and $ 12.40 per employee for dental insurance.

Solution Summary: The author calculates the total weekly cost of fringe benefits of dynamo productions.

Concept explainers

Videos

To calculate: The total weekly cost of fringe benefits of dynamo productions. They employ 250 workers with gross payroll of $123,400 per week with fringe benefits are 5% of gross payroll for sick days and holiday leave 8% for health insurance and $12.40 per employee for dental insurance.

To calculate: The percentage of payroll $123,400 the fringe benefit $19,142 represent.

To calculate: The cost of fringe benefit $19,142 for one year.

Chapter 9 Solutions

To calculate: The total weekly cost of fringe benefits of dynamo productions. They employ 250

workers with gross payroll of $123,400 per week with fringe benefits are 5% of gross payroll

for sick days and holiday leave 8% for health insurance and $12.40 per employee for dental

insurance.