(a) The following diagram shows the movement of Kenyan households among three income groups: affluent, middle class, and poor, over the 11-year period 1980-1991. AFFLUENT 27.1% Sh72,000 (in 1994) 7.5% MIDDLE CLASS 8.5% Sh24,000 (in 1994) 30.4% POOR (i) Use the transitions shown in the diagram to construct a transition matrix (assuming zero probabilities for the transitions between affluent and poor). (ii) Assuming that the trend shown was to continue, what percent of households' classified as affluent in 1980 -1991, were predicted to become poor in 1993? (iii) According to the model, what percentage of all Kenyan households will be in each income bracket in the long term?

(a) The following diagram shows the movement of Kenyan households among three income groups: affluent, middle class, and poor, over the 11-year period 1980-1991. AFFLUENT 27.1% Sh72,000 (in 1994) 7.5% MIDDLE CLASS 8.5% Sh24,000 (in 1994) 30.4% POOR (i) Use the transitions shown in the diagram to construct a transition matrix (assuming zero probabilities for the transitions between affluent and poor). (ii) Assuming that the trend shown was to continue, what percent of households' classified as affluent in 1980 -1991, were predicted to become poor in 1993? (iii) According to the model, what percentage of all Kenyan households will be in each income bracket in the long term?

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Concept explainers

Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!

Question

(a) The following diagram shows the movement of Kenyan households among
three income groups: affluent, middle class, and poor, over the 11-year
period 1980–1991.
AFFLUENT
27.1%
Sh72,000
(in 1994)
7.5%
MIDDLE CLASS
8.5%
Sh24,000
(in 1994)
30.4%
POOR
(i)
Use the transitions shown in the diagram to construct a transition
matrix (assuming zero probabilities for the transitions between
affluent and poor).
(ii)
Assuming that the trend shown was to continue, what percent of
households' classified as affluent in 1980 -1991, were predicted to
become poor in 1993?
(iii)
According to the model, what percentage of all Kenyan households
will be in each income bracket in the long term?

(c) A two sector economy has the following input-output technical matrix
R0.4
0.3
s 0.6
The final demand for the next year is estimated as sh 60 million for
sector R and sh 90 million for sector S. Determine
(i) Total production from each sector in order to satisfy both
intermediate and final demand.
(ii)Total worth of primary inputs for the production level in (i)
(iii)
Account for the usage of sector R output
(iv)
Account for the sources of sector Q input

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In a survey, it was found that 72%of the population of a certain urban area lived in single-family dwellings and 28% in multiple housing. One year later, of those who had been living in single-family dwellings, 89%still did so, but 11% had moved to multiple-family dwellings. Of those in multiple housing, 94%were still living in that type of housing, while 6%had moved to single-family housing. Assume that these trends continue. (a) Write a transition matrix using this information. Set it up so that the first row and first column represent single-family dwellings and the second row and second column represent multiple housing.
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