Respuesta :
The probability that the device fails during its first hour of operation is; 0.625
How to Calculate Joint Density Function?
The joint density function of the lifetimes of the two components, both measured in hours, is:
f(x, y) = (x + y)/8; 0 < x < 2, 0 < y < 2
Compute the probability that the device fails during its first hour of operation as follows:
P[(X < 1) ∪ (Y < 1)] = 1 - [tex]\int\limits^2_1 {} \int\limits^2_1 {\frac{x + y}{8} } \, dx \, dy[/tex]
Integrating the above with respect to the boundary conditions as above gives;
P[(X < 1) ∪ (Y < 1)] = 1 - 0.375
P[(X < 1) ∪ (Y < 1)] = 0.625
The complete question is;
A device runs until either of two comonents fails, at which point the device stops running. The joint density function of the lifetimes of the two components, both measured in hours, is f(x,y) = x + y/8 for 0 < x < 2 and 0 < y < 2Calculate the probability that the device fails during its first hour of operation.
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