Adevice containing two key components fails when and only when both components fail. the lifetimes, t1 and t2, of these components are independent with common density function f(t)=e^-t for t > 0. the cost, x, of operating the device until failure is 2t1 + t2.
1. what is the density function of x for x > 0?

Step-by-step explanation:

If we have two random variables Y1 and Y2 and we have th following limits:

We an find the density function with this formula:

Now for our problem we know that for the two times of failure the density function is given by:

And we know that the joint density for T1 and T2 is given by:

And we know that

If we solve for

And then we can find the density function like this:

2 & 7

step-by-step explanation:

he climbs 300 ft/hr at a constant rate. the peak is at 1,500 ft.

when going up, he reaches 600 ft in 2 hours. remember, that he is going in a constant rate. divide 600 with 300:

600/300 = 2

assuming that he takes the same route back (meaning that it's a 1500 ft route back, you can solve.

note also that you are solving when he gets back to 600 ft after he reaches the peak.

first, find the amount of hours it takes to get up the peak. divide the total amount (1500), with the ft/her (300) to get the amount of hours (x):

1500/300 = x

x = 5

it takes jamie 5 hours to get up. now, he is returning down, and reaches 600 (his current destination). remember that he climbs at a constant 300 ft/hr. divide 600 with 300:

600/300 = x

x = 2

now add the two numbers together.

x = 5 + 2 = 7

jamie takes 7 hours to go up the mountain and reach his current position when descending.

(total amount/constant rate) = (time).

remember that it is a constant rate, so in total, when he gets back down the mountain, it will take the same amount of time as when he goes up. the total amount for the round trip is: 5 + 5 = 10.

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