Female life expectancy . Refer to Problem 91 . Subsequent data indicated that life expectancy grew to 79.1 years for females born during 1995 - 2000 and to 79.7 years for females born during 2000 - 2005 . Add the points 15 , 79.1 , and 20 , 79.7 to the data set in Problem 91 . Using a graphing calculates to find a quadratic regression model for all foe data points. Graph the data and the model in the same viewing window.
Female life expectancy . Refer to Problem 91 . Subsequent data indicated that life expectancy grew to 79.1 years for females born during 1995 - 2000 and to 79.7 years for females born during 2000 - 2005 . Add the points 15 , 79.1 , and 20 , 79.7 to the data set in Problem 91 . Using a graphing calculates to find a quadratic regression model for all foe data points. Graph the data and the model in the same viewing window.
Solution Summary: The author explains how to calculate the quadratic equation for the data of life expectancy for females.
Female life expectancy. Refer to Problem
91
. Subsequent data indicated that life expectancy grew to
79.1
years for females born during
1995
-
2000
and to
79.7
years for females born during
2000
-
2005
. Add the points
15
,
79.1
,
and
20
,
79.7
to the data set in Problem
91
. Using a graphing calculates to find a quadratic regression model for all foe data points. Graph the data and the model in the same viewing window.
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, ....
Chapter 4 Solutions
Pearson eText for Finite Mathematics for Business, Economics, Life Sciences, and Social Sciences -- Instant Access (Pearson+)
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