At a seismogram in a given time window the signals reflected from horizons A and B are observed. The statistical properties of noise are those, that the signal from horizon A is distorted on the...

At a seismogram in a given time window the signals reflected from horizons A and B are observed. The statistical properties of noise are those, that the signal from horizon A is distorted on the average with probability 2/5, and from horizon B with probability 1/5. The analysis of the seismograms of the neighboring region has shown, that appearance the signal from horizon A is in the relation 3:7 to the signal from horizon B. To find the probabilities

(a) the locked-on signal is generated by the horizon A,

(b) the locked-on signal is generated by the horizon B.

The random variable ξ obeys the Cauchy distribution with the density function

The variable η is interlinked with ξ by the relation

To find a density function of the random variable η.