Probability of x failing before y

In summary, the conversation discusses a problem involving the failure of two components, X and Y, that are independent of each other. The density of X is given by f(x)=exp(-x), and the density of Y is given by f(y)=2*exp(-2y). The question is, what is the probability that X fails first? The conversation also mentions trying to find the probability of X failing and Y not failing at a certain time T, but the speaker is stuck on how to solve the problem.
  • #1
tony3333
4
0

Homework Statement



hi,
i have a problem and i really want you to help me with it.
we have X and Y that fail independently of each other.
density of X : f(x)=exp(-x), and density of Y : f(y)=2*exp(-2y) what is the probability that X component fails first?
(it should be a number)
thank you
 
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  • #2
You need to show some work. What have you tried?
 
  • #3
so, i think, i need the probability of X failing and Y not, at a time T.
T T T oo
so it is Pr=∫f(x)dx *(1-∫f(y)dy)=∫2*exp(-2t)dt * ∫2*exp(-2t)dt=
0 0 0 T
and here i am stuck...


(the limits of the first integral are (0,T), second (0,T), third (0,T), and forth (T, +oo)
 

1. What is the "Probability of x failing before y"?

The "Probability of x failing before y" is a mathematical concept that measures the likelihood of one event happening before another event in a series of events. It is typically represented as a ratio or percentage and is used in various fields such as finance, engineering, and statistics.

2. How is the "Probability of x failing before y" calculated?

The "Probability of x failing before y" is calculated by dividing the number of outcomes where x fails before y by the total number of possible outcomes. This can be represented as a ratio, decimal, or percentage. The calculation may vary depending on the specific scenario and the type of probability being used (e.g. conditional probability, independent probability, etc.).

3. What does a high "Probability of x failing before y" mean?

A high "Probability of x failing before y" means that there is a greater chance of x failing before y in a series of events. This could indicate that x is more likely to occur earlier in the series or that y is more likely to occur later. It is important to note that a high probability does not guarantee that x will fail before y, as there is always a chance for unexpected outcomes.

4. Can the "Probability of x failing before y" change over time?

Yes, the "Probability of x failing before y" can change over time. This is because the probability is influenced by various factors such as the number of events, the specific conditions of the events, and any changes in those conditions. As these factors change, the probability of x failing before y may also change.

5. How can the "Probability of x failing before y" be applied in real life?

The "Probability of x failing before y" can be applied in various real-life situations, such as predicting the likelihood of a certain event happening before another event (e.g. a machine breaking down before its scheduled maintenance). It can also be used in decision-making processes, risk analysis, and other scenarios where understanding the probability of one event occurring before another is important.

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