30 Points Yaz Scream Whose Dominant Frequency Gaussian Random Variable Mean 2000 Hz Stand Q32942653

. (30 points) Yaz has a scream whose dominant frequency is aGaussian random variable with mean 2000 Hz and standard deviation100 Hz. Ryan has a scream whose dominant frequency is a Gaussianrandom variable with mean 1800 Hz and standard deviation 75 Hz.Ryan is also more excitable than Yaz, so the prior probability PRthat a scream comes from Ryan is 0.85 (and from Yaz is PY = 1−PR =0.15). The Doctor now hears a scream whose dominant frequency is1925 Hz.

(a) (10 points) Who does the Doctor decide screamed if sheapplies the Bayes Decision Rule?

(b) (10 points) Determine the frequency above which the Doctorwill always choose Yaz if she applies the Bayes Decision Rule.(Hint: you can use WolframAlpha to solve the necessaryequation.)

(c) (10 points) Compute the overall probability of error for thedecision rule in (b). (Note: this requires Q functions.)