Set up the migration matrix for this situation, using five decimal places for th

Question

Set up the migration matrix for this situation, using five decimal places for the migration rates into and out of California for the following:

In 1994, California was 31,524,000 and the population living in the United States but outside California was 228,680,000. During the year, it is estimated that 516,000 persons moved from California to elsewhere in the U.S. while 381,262 persons moved to California from elsewhere in the U.S.

The answer is M =[    0.9836    .0017  ]

                                  0.01634     .9983

M being the migration matrix...

How did they get M? Please show all steps and calculations.

Explanation / Answer

The two places dealt here are not California and California

In 1994 the number of people living in California = 31,524,000

During this year, it is estimated that 516,000 persons moved from California to elsewhere

Hence Probability (proportion) of people moved from California to someplace else in US = 516,000/31,524,000

= 0.01634

Proportion of people who stayed back in California = 1-0.01634 = 0.9836

population living in the United States but outside California was 228,680,000

381,262 persons moved to California from elsewhere in the U.S.

Hence Probability (proportion) of people moved to California from elsewhere in the U.S. = 381,262/228,680,000

= 0.0017

Proportion of people who stayed back in someplace else other than California = 1-0.0017 = 0.9983

Hence the migration matrix is

M =[ 0.9836   .0017  ]

[ 0.01634   .9983 ]

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