show that if {X (t), t≥ 0} is a stochastic process with independent processes, then the...

show that if {X (t), t≥ 0} is a stochastic process with independent processes, then the process defined by Y (t) = X (t) - X (0), for t≥ 0, has independent increments and Y(0)=0

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Colby Messinger answered 2 years ago

Q1. Let {Xt |t ∈ [0, 1]} be a stochastic process such that EX2 t <...

Q1. Let {Xt |t ∈ [0, 1]} be a stochastic process such that EX2 t < ∞ for all t ∈ [0, 1] which is strictly stationary. Show that it is stationary . Q2. Let {Xt |t ∈ I} be strictly stationary. Prove or disprove that process is with stationary increments. Q3. Let {Xt |t ∈ I} be with stationary increments. Prove or disprove that the process is stationary. Q4. Prove or disprove that the stochastic process {Xn|n ≥ 0},...

Assume that the Poisson process X = {X(t) : t ≥ 0} describes students’ arrivals at...

Assume that the Poisson process X = {X(t) : t ≥ 0} describes students’ arrivals at the library with intensity λ = 4 per hour. Given that the tenth student arrived exactly at the end of fourth hour, or W10 = 4, find: 1. E [W1|W10 = 4] 2. E [W9 − W1|W10 = 4]. Hint: Suppose that X {X(t) : t ≥ 0} is a Poisson process with rate λ > 0 and its arrival times are defined for...

Solve the following differential equations: 1.) y"(x)+ y(x)=4e^x ; y(0)=0, y'(0)=0 2.) x"(t)+3x'(t)+2x(t)=4t^2 ; x(0)=0, x'(0)=0

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show that if {X (t), t≥ 0} is a stochastic process with independent processes, then the...

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Q1. Let {Xt |t ∈ [0, 1]} be a stochastic process such that EX2 t <...

Assume that the Poisson process X = {X(t) : t ≥ 0} describes students’ arrivals at...

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Solve the following differential equations: 1.) y"(x)+ y(x)=4e^x ; y(0)=0, y'(0)=0 2.) x"(t)+3x'(t)+2x(t)=4t^2 ; x(0)=0, x'(0)=0