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Asked Nov 15, 2019
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6. Let {N(t) t 2 0} be a Poisson process with rate AX that is independent of the nonnegative
random variable T with mean u and variance o2. Find
(a) Cov(T, N(T)),
(b) Var(N(T)
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6. Let {N(t) t 2 0} be a Poisson process with rate AX that is independent of the nonnegative random variable T with mean u and variance o2. Find (a) Cov(T, N(T)), (b) Var(N(T)

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Expert Answer

Step 1

As per question, N(T) is a poisson process with rate λ and it is independent of the nonnegative random variable T with mean µ and variance σ2.

a)

T and N(T) are independent, then they are not correlated with each other, so

Cov(T,N(T))  = 0

⸪ Covariance is zero for independent variables.

Step 2

b) Variance of a poisson distribution with parameter λ is λ...

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