Sheldon M Ross Stochastic: Process 2nd Edition Solution

4.3. Consider a Markov chain with states 0, 1, and 2, and transition probability matrix:

Solution:

E[X] = ∫[0,1] x(2x) dx = ∫[0,1] 2x^2 dx = (2/3)x^3 | [0,1] = 2/3 Sheldon M Ross Stochastic Process 2nd Edition Solution

Find PX2 = 2 .

E[X(t)] = E[A cos(t) + B sin(t)] = E[A] cos(t) + E[B] sin(t) = 0 1] x(2x) dx = ∫[0

Var(X) = E[X^2] - (E[X])^2 = ∫[0,1] x^2(2x) dx - (2/3)^2 = ∫[0,1] 2x^3 dx - 4/9 = (1/2)x^4 | [0,1] - 4/9 = 1/2 - 4/9 = 1/18 Sheldon M Ross Stochastic Process 2nd Edition Solution

Solution: