Consider the birth and death process with the following mean rates The birth rates are 0 2, 1 3, 2 2, 3 1, and n 0 for n 3 The death rates are 1 3, 2 4, 3 1, and n 2 for n 4 (a) Construct the rate diagram for this birth and death process (b) Develop the balance equations (c) Solve these equations t...

a b 1 2P 0 3P 1 2 2P 0 4P 2 6P 1 3 3P 1 P 3 6P 2 4 2 ...

Consider the birth-and-death process with the following mean rates. The birth rates are 0 = 2, 1

Question:

Consider the birth-and-death process with the following mean rates. The birth rates are λ0 = 2, λ1 = 3, λ2 = 2, λ3 = 1, and λn = 0 for n > 3. The death rates are μ1 = 3, μ2 = 4, μ3 = 1, and μn = 2 for n > 4.
(a) Construct the rate diagram for this birth-and-death process.
(b) Develop the balance equations.
(c) Solve these equations to find the steady-state probability P0, P1, . . . .
(d) Use the general formulas for the birth-and-death process to calculate P0, P1, . . . . Also calculate L, Lq, W, and Wq.
Distribution
The word "distribution" has several meanings in the financial world, most of them pertaining to the payment of assets from a fund, account, or individual security to an investor or beneficiary. Retirement account distributions are among the most...