Exercise3.6 A reactiontimeforacertainstimulusforbothcatsanddogsisknowntobeexpo- nentially distributed.Inaddition,biologistsbelievethatanaveragereactiontimeforcatsis times fasterthanthatfordogs.Abiologistperformedaseriesofexperimentsandmeasuredthereaction times X1, ...,Xn of n dogs and Y1, ...,Ym

Exercise3.6 A reactiontimeforacertainstimulusforbothcatsanddogsisknowntobeexpo-

nentially distributed.Inaddition,biologistsbelievethatanaveragereactiontimeforcatsis ρ times fasterthanthatfordogs.Abiologistperformedaseriesofexperimentsandmeasuredthereaction times X1, ...,Xn of n dogs and Y1, ...,Ym of m cats.

1. Find theMLEforaveragereactiontimesofdogsandcats.

2. Construct 100(1−α)% confidenceintervalsforaveragereactiontimesofdogsandcats.

(Hint: thedistributionsof Σn i=1 Xi and Σmj

=1Yj may beuseful.)

3. Assume nowthat ρ is unknown.FinditsMLEanda100(1−α)% confidenceintervalforit.

(Hint: recalltherelationshipsbetween χ2 and the F-distribution.)