1. Currently there are 3 investment plans available for the employees of a compa
ID: 3047356 • Letter: 1
Question
1. Currently there are 3 investment plans available for the employees of a company: A, B, and C. An employee can use one plan at a time and may switch from one plan to another only at the end of the year. The probability that someone in plan A will continue in plan A is 20%, switch from A to B is 20%, switch from A to C is 60%. The probability that someone in plan B will continue in plan B is 50%, switch from B to A is 50%, switch from B to C is 0%. The probability that someone in plan C will continue in plan C is 50%, switch from C to B is 0%, switch from C to A is 50%. (a) (8 pts) Find the stochastic matrix P (b) (2 pts) If xo (2, .6, 2) is the initial employee distribution in the three plans, find the distribution after 4 years. (c) (2 pts) Is the stochastic matrix a regular stochastic matrix? Why or why not? (d) (8 pts) What will the long-term distribution be for the three plans, i.e., what's the steady-state vector? Find the exact values algebraically.Explanation / Answer
From given data the corresponding stochastic matrix can be written as follows:
Plan
A
B
C
A
0.20
0.20
0.60
B
0.50
0.50
0
C
0.50
0
0.50
X0 M4 = [0.383120.179220.43766]
M25 =
0.38461540.15384620.4615385
0.38461540.15384620.4615384
0.38461540.15384610.4615385
Hence after 25 years, 38% employees of company A will continue with A, 15% of company B will continue with B and 46% of company C will continue with C.
Plan
A
B
C
A
0.20
0.20
0.60
B
0.50
0.50
0
C
0.50
0
0.50
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