Eighty thousand, two hundred eighty-one in numeric form.

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Answer 1

Question

Chapter 1.1, Problem 2AH

a.

To determine

To write: Eighty thousand, two hundred eighty-one in numeric form.

b.

To determine

To write: Fifty-eight thousand, three in numeric form.

c.

To determine

To write: Two hundred eighty thousand, five in numeric form.

d.

To determine

To write: Three million, ten in numeric form.

e.

To determine

To write: Sixty-seven thousand, seven hundred sixty in numeric form.

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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 1.1, Problem 2AH

a.

To determine

To write: Eighty thousand, two hundred eighty-one in numeric form.

b.

To determine

To write: Fifty-eight thousand, three in numeric form.

c.

To determine

To write: Two hundred eighty thousand, five in numeric form.

d.

To determine

To write: Three million, ten in numeric form.

e.

To determine

To write: Sixty-seven thousand, seven hundred sixty in numeric form.

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Answer 3

Question

Chapter 1.1, Problem 2AH

a.

To determine

To write: Eighty thousand, two hundred eighty-one in numeric form.

b.

To determine

To write: Fifty-eight thousand, three in numeric form.

c.

To determine

To write: Two hundred eighty thousand, five in numeric form.

d.

To determine

To write: Three million, ten in numeric form.

e.

To determine

To write: Sixty-seven thousand, seven hundred sixty in numeric form.

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Answer 4

Question

Chapter 1.1, Problem 2AH

a.

To determine

To write: Eighty thousand, two hundred eighty-one in numeric form.

b.

To determine

To write: Fifty-eight thousand, three in numeric form.

c.

To determine

To write: Two hundred eighty thousand, five in numeric form.

d.

To determine

To write: Three million, ten in numeric form.

e.

To determine

To write: Sixty-seven thousand, seven hundred sixty in numeric form.

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Answer 5

Chapter 1.1, Problem 2AH

a.

To determine

To write: Eighty thousand, two hundred eighty-one in numeric form.

b.

To determine

To write: Fifty-eight thousand, three in numeric form.

c.

To determine

To write: Two hundred eighty thousand, five in numeric form.

d.

To determine

To write: Three million, ten in numeric form.

e.

To determine

To write: Sixty-seven thousand, seven hundred sixty in numeric form.

Answer 6

Chapter 1.1, Problem 2AH

a.

To determine

To write: Eighty thousand, two hundred eighty-one in numeric form.

Answer 7

Chapter 1.1, Problem 2AH

a.

To determine

To write: Eighty thousand, two hundred eighty-one in numeric form.

Answer 8

b.

To determine

To write: Fifty-eight thousand, three in numeric form.

Answer 9

b.

To determine

To write: Fifty-eight thousand, three in numeric form.

Answer 10

c.

To determine

To write: Two hundred eighty thousand, five in numeric form.

Answer 11

c.

To determine

To write: Two hundred eighty thousand, five in numeric form.

Answer 12

d.

To determine

To write: Three million, ten in numeric form.

Answer 13

d.

To determine

To write: Three million, ten in numeric form.

Answer 14

e.

To determine

To write: Sixty-seven thousand, seven hundred sixty in numeric form.

Answer 15

e.

To determine

To write: Sixty-seven thousand, seven hundred sixty in numeric form.

Answer 16

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Answer 17

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Answer 18

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Answer 19

Ch. 1.1 - Write in verbal form: 7,948 ...Ch. 1.1 - Prob. 2PQ Ch. 1.1 - Kellogg’s reported its sales as five million, one...Ch. 1.1 - Write in verbal form: 8,682 ...Ch. 1.1 - Prob. 2EPQ Ch. 1.1 - Kellogg’s reported its sales as three million, two...Ch. 1.1 - Express the following numbers in verbal...Ch. 1.1 - Write in numeric form: Eighty thousand, two...Ch. 1.1 - Round the following numbers: To the nearest...Ch. 1.1 - Round off each number to the nearest ten, nearest...

Eighty thousand, two hundred eighty-one in numeric form.

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To write: Eighty thousand, two hundred eighty-one in numeric form.

To write: Fifty-eight thousand, three in numeric form.

To write: Two hundred eighty thousand, five in numeric form.

To write: Three million, ten in numeric form.

To write: Sixty-seven thousand, seven hundred sixty in numeric form.

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Chapter 1 Solutions