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Sheldon M Ross Stochastic Process 2nd Edition Solution Link

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

Below are some sample solutions to exercises from the second edition of "Stochastic Processes" by Sheldon M. Ross: Sheldon M Ross Stochastic Process 2nd Edition Solution

Autocov(t, s) = E[(X(t) - E[X(t)]) (X(s) - E[X(s)])] = E[X(t)X(s)] = E[(A cos(t) + B sin(t))(A cos(s) + B sin(s))] = E[A^2] cos(t) cos(s) + E[B^2] sin(t) sin(s) = cos(t) cos(s) + sin(t) sin(s) = cos(t-s) Var(X) = E[X^2] - (E[X])^2 = ∫[0,1] x^2(2x)

E[X(t)] = E[A cos(t) + B sin(t)] = E[A] cos(t) + E[B] sin(t) = 0 Sheldon M Ross Stochastic Process 2nd Edition Solution

Solution:

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

Below are some sample solutions to exercises from the second edition of "Stochastic Processes" by Sheldon M. Ross:

Autocov(t, s) = E[(X(t) - E[X(t)]) (X(s) - E[X(s)])] = E[X(t)X(s)] = E[(A cos(t) + B sin(t))(A cos(s) + B sin(s))] = E[A^2] cos(t) cos(s) + E[B^2] sin(t) sin(s) = cos(t) cos(s) + sin(t) sin(s) = cos(t-s)

E[X(t)] = E[A cos(t) + B sin(t)] = E[A] cos(t) + E[B] sin(t) = 0

Solution:

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