Froghas ansqueak that its dominant frequency is a Gaussian random variable, and itsmean is 4000 Hz and standard deviation is 200 Hz. Bird has an squeak that itsdominant frequency is a Gaussian random variable and itsmean is 4400 Hz and standard deviation is 400 Hz. The prior probability PF that a squeak comes from Frogis 0.75 (and from Bird is PY = 1PF = 0.25). Ian now hears a squeak thatdominant frequency is 4300 Hz.

(a)Who does the Ian decide squeaked if he applies the Maximum Likelihood Decision Rule?

(b)Who does the Ian decide squeaked if he applies the Bayes Decision Rule?

(c) Determine the frequency above which the Ian will always choose Bird if he applies the Bayes Decision Rule.

(d)Compute the overall probability of error for the decision rule in (c). (Note: this requires Q functions.)