just part a plz thank u! Page 4 Marks Suppose Z(t) Y., where X(t) is the Poisson process with rate θ If μ = E[h] and σ2-Yar determine the mean and variance of Z(t) a. pil are the common mean and v...

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just part a plz thank u!
Page 4 Marks Suppose Z(t) Y., where X(t) is the Poisson process with rate θ If μ = E[h] and σ2-Yar determine the mean and var

math Statistics-And-Probability

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Answer #1

E(Z(T)) = $E(\sum_{K=1}^{x(t)} Y$ _K) = E( Y₁₊Y₂ + Y₃ + ........+Y_X(t) ) = E(Y₁) + E(Y₂) + .........+ E(Y_X(t) ) = $\mu + \mu ......+ \mu$ = X(t)* $\mu$

Var(Z(T)) = $VAR(\sum_{K=1}^{X(t)}Y$ _K) = VAR( Y₁₊Y₂ + Y₃ + ........+Y_X(t) ) = V(Y₁) + V(Y₂) + .........+ V(Y_X(t) ) = = X(t)* $\sigma ^{2}$

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just part a plz thank u! Page 4 Marks Suppose Z(t) Y., where X(t) is the Poisson process with rate θ If μ = E[h] and σ2-Yar determine the mean and variance of Z(t) a. pil are the common mean and v...

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just part a plz thank u! Page 4 Marks Suppose Z(t) Y., where X(t) is the Poisson process with rate θ If μ = E[h] and σ2-Yar determine the mean and variance of Z(t) a. pil are the common mean and v...