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revAdmin (Created page with "'''Answer: E''' <math>E[Z]=\int_{0}^{\infty} b_{t} \cdot v^{t} \cdot{ }_{t} p_{x} \cdot \mu_{x+t} d t=\int_{0}^{\infty} e^{0.02 t} \cdot e^{-0.06 t} \cdot e^{-0.04 t} \cdot 0.04 d t</math> <math>=0.04 \int_{0}^{\infty} e^{-0.08 t} d t=\frac{0.04}{0.08}=\frac{1}{2}</math> <math>E\left[Z^{2}\right]=\int_{0}^{\infty}\left(b_{t} \cdot v^{t}\right)^{2}{ }_{t} p_{x} \cdot \mu_{x+t} d t=\int_{0}^{\infty}\left(e^{0.04 t}\right)\left(e^{-0.12 t}\right)\left(0.04 e^{-0.04}\righ...")Jan 18'24 at 12:18+638