Statistically independent confusion

In summary, the conversation discusses the probability of a communication system successfully sending signals from 'a' to 'b' over 2 parallel paths with 2 repeaters each. The repeaters have independent failure probabilities and the overall failure probability is calculated by multiplying the individual failure rates of each path. The concept of statistically independent events and calculating failure rates in different configurations is also mentioned.
  • #1
alibabamd
2
0
hey guys,
tell me how i would approach this:
a communication system sends signals from 'a' to 'b' over 2 parallel paths. If each path has 2 repeaters with failure probablities X for the first path repeaters ,Y for the second path repeaters then what would be the probability of signal not arriving at all. The repeaters are statistically independent.

I thought it would be X*X+Y*Y.
However, i thought that if one repeater fails it won't matter if the second one fails. So they can't be statsically independent right? So how would one go about doing this?
 
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  • #2
Path 1 success: (1-X)^2
Path 1 failure: 1 - (1-X)^2

Path 2 success: (1-Y)^2
Path 2 failure: 1 - (1-Y)^2

Overall failure probability: (1 - (1-X)^2) * (1 - (1-Y)^2)
 
  • #3
ok so you're also taking them as statistically independent right, its just that i was thnking if the first repeater fails doesn't that automatically mean the second won't transmit correctly... thanks for the quick reply though
 
  • #4
I understand what you're saying and I think my formulas address that. In calculating the failure rate I'm saying if either repeater fails the link as a whole fails.

By multiplying the failure rates of both links, I'm saying that if either link succeeds the message gets through.

In general to calculate two independent failures in an AND configuration as in the two repeaters in series, you have to multiply the success probabilities and subtract from one to get the failure rate. To calculate failure rates in parallel or in and OR configuration, multiply the failure probabilities.
 
  • #5
If "2 parallel paths" means what I think it means, the only way a signal won't go through is if BOTH repeaters fail. As long as at least one works the signal will go through.
 

1. What is statistically independent confusion?

Statistically independent confusion refers to the phenomenon where two or more variables are not causally related, but their values are still correlated. In other words, there is no direct relationship between the variables, but they still tend to occur together due to chance.

2. How does statistically independent confusion impact statistical analyses?

Statistically independent confusion can affect statistical analyses by creating the appearance of a relationship between variables which may not actually exist. This can lead to misleading conclusions and incorrect interpretations of data.

3. What causes statistically independent confusion?

Statistically independent confusion can be caused by a variety of factors, including small sample sizes, measurement errors, and confounding variables. It can also occur when there is a lack of understanding or consideration of the underlying mechanisms and relationships between variables.

4. Can statistically independent confusion be avoided?

While it may not be possible to completely avoid statistically independent confusion, there are steps that can be taken to minimize its impact. This includes carefully designing experiments and studies, using appropriate statistical methods, and considering potential confounding variables.

5. How can we address statistically independent confusion in research?

In order to address statistically independent confusion in research, it is important to thoroughly examine and understand the relationships between variables. This can involve conducting further analyses, controlling for confounding variables, and replicating studies to ensure the validity of results.

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