Need help with one problem regarding PDF (probability Density function)

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Navi1999

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I'd appreciate your help, i've been looking for solutions but can't find any. Here is the problem:

The lifespan of a machine has a pdf of:

Captura de Pantalla 2020-08-31 a la(s) 3.47.00.png


a) What is the probability that the machine will still be alive after 5 years?

b) What is the probability that the machine "dies" between 3rd and 6th year since it started working?


Thank you. Would appreciate if you can explain it deeply so I can understand and learn better :D
 
Before looking for solutions, let's look for understanding.

Do you know what a pdf means? How is the probability P( x>5 ) related to the pdf? Tell us what you know, and we can base our answers on that.
 
Dr.Peterson said:
Before looking for solutions, let's look for understanding.

Do you know what a pdf means? How is the probability P( x>5 ) related to the pdf? Tell us what you know, and we can base our answers on that.
Click to expand...
Yes I have resolved some pdf problems already but they are very different for this one I dont even know where to start. Cant find any similar question on my textbook
 
Navi1999 said:
Yes I have resolved some pdf problems already but they are very different for this one I dont even know where to start. Cant find any similar question on my textbook
Click to expand...
The place to start is with what you know. That's why I asked what you know (not just whether you know!) about the pdf. Writing down some facts can help you get started.

Also, relating the problem to what you know will help you see how some examples in your book are in fact similar to this question, at a deeper level. Often students look for superficially similar problems (in this case, perhaps about the lifespan of a machine) rather than seeing the real form of a problem. So here, you might translate the problem into more general terms, removing the specifics. "What is the probability that the machine will still be alive after 5 years?" becomes "What is the probability that the lifespan is greater than 5 years?", which in turn becomes "What is P(x>5)?" That is where my question came from, and why it is important.

In turn, if you only know, say, how to find P(x<5) from a pdf, you can now think about how the two probabilities are related.

So, do you have any ideas yet?
 
I am also surprised that the problem gives the PDF in terms of "x" without any indication as to whether x is in "years" or "days" or whatever units (It might even be that "x" is a distance it feet! We don't know!) and then asks about what happens in 5 years.
 
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