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

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8 views help_outlineImage Transcriptionclose6. 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) fullscreen
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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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