Question

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 and 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.)

Answer 1

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

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

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