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.)

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

Step-by-step explanation:

probability for X (for x≥ 0)

e⁻ˣ

Probability for X exceed 3

=

=

=

probabilty for y≥ 0 is

+25 = x

step-by-step explanation:

here x is the hypotenuse of a right triangle whose legs are 7 and 24.   by the pythagorean theorem, 7² + 24² must equal x²:

x² = 49 + 576 = 625.   thus, x = +√625 = +25 = x