Hello all,

I want to have a better understanding of max and min.

So far, I see min as the subset and max as something that is overlaying.

I'm not absolutely sure about that.

On SOA 153, #46.

A device that continuously measures and records seismic activity is placed in a remote

region. The time, T, to failure of this device is exponentially distributed with mean

3 years. Since the device will not be monitored during its first two years of service, the

time to discovery of its failure is X = max(T, 2) .

Determine E[X].

Solution goes as:

I know the pdf of expo(1/3) and how to generally get EX.

But they add two integrals:

int(2f(x) from 0, 2) + int(xf(x) from 2,inf).

f(x) = pdf of expo(1/3)

Why is int(2f(x) from 0, 2) included? Where does the multiplier 2 come from?

thanks

I want to have a better understanding of max and min.

So far, I see min as the subset and max as something that is overlaying.

I'm not absolutely sure about that.

On SOA 153, #46.

A device that continuously measures and records seismic activity is placed in a remote

region. The time, T, to failure of this device is exponentially distributed with mean

3 years. Since the device will not be monitored during its first two years of service, the

time to discovery of its failure is X = max(T, 2) .

Determine E[X].

Solution goes as:

I know the pdf of expo(1/3) and how to generally get EX.

But they add two integrals:

int(2f(x) from 0, 2) + int(xf(x) from 2,inf).

f(x) = pdf of expo(1/3)

Why is int(2f(x) from 0, 2) included? Where does the multiplier 2 come from?

thanks

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