The future lifetimes (in months) of two components of a machine have the following joint density function: f(x, y) = {6/125,000 (50 - x - y) for 0 < x < 50 - y < 50, 0 otherwise. Write down a single integral representing the probability that both components are still functioning in 20 months from now.

Here is the correct computation of the question.

The future lifetimes (in months) of two components of a machine have the following joint density function:

 for 0 < x < 50 - y < 50, otherwise.

Write down a single integral representing the probability that both components are still functioning in 20 months from now.

Step-by-step explanation:

From the given information;

 for 0 < x < 50 - y < 50, otherwise.

We can assert that the probability is the integral of the given density over the part of the range  0 ≤ x ≤ 50 - y ≤ 50 in which  both x and y are greater than 20.

From the attached file below; their shows a probability density graph illustrating the above statement being said.

Now; to determine the probability that illustrates the integral of the density ; we have : P[(X > 20)∩(Y > 20)]

In addition to that:

From the image attached below;

We look into the region where the joint density under study is said to be positive and the triangle limits by the line axis x+y = 50

∴

Thus; the  single integral representing the probability that both components are still functioning in 20 months from now is

x intercept = (-1,0)   (4,0)

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step-by-step explanation: