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I read the following problem and I cannot get the right solution:

We consider a system of 12 sensors. The probability of one sensor to detect a signal with a magnitude higher than a is $p=\frac{1}{2\pi }\int_{x=a}^\infty \exp(\frac{-x^2}{2})$. What is the joint probability that 5 sensors detect this signal? It is stated that if a=2.8, the five signals yield to a joint probability corresponding to 5.7

Thanks!

1 Answers 1