Statistically independent confusion

[alibabamd]

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?

 

[skeptic2]

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)

 

[alibabamd]

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

 

[skeptic2]

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.

 

[statdad]

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.