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dangina [55]
3 years ago
12

Two components of a minicomputer have the following joint pdf for their useful lifetimes X and Y: f(x, y) = xe−x(1 + y) x ≥ 0 an

d y ≥ 0 0 otherwise (a) What is the probability that the lifetime X of the first component exceeds 4? (Round your answer to three decimal places.)
Mathematics
1 answer:
Yuri [45]3 years ago
3 0

Answer:

For the given explanation we see that two life times are not independent

Step-by-step explanation:

probability for X (for x≥ 0)

\int\limits^\infty_0 {xe^-^x^(^1^+^y^)} \, dy

-e^-^x\int\limits^\infty_0 {de^-^x^y} \,

e⁻ˣ

Probability for X exceed 3

= \int\limits^\infty_3 {f(x)dx

= \int\limits^\infty_3 {e^-^3 dx

= e^-^3

probabilty for y≥ 0 is

\int\limits^\infty_0 {xe^-^x^(^1^+^y^)} \, dx \\

\int\limits^\infty_0{-x/1+yd(e^-^x^(^1^+^y^))} \, =1/(1+y)² \\

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