2. Iocane or Sennari. An absent-minded chemistry professor forgets to label two identically looking bottles. One contains a chemical named "Iocane" and the other contains a chemical named "Sennari". It is well known that the radioactivity level of "Iocane" has the Unif[0,1] distribution, while the radioactivity level of "Sennari" has the Exp(1) distribution. (a) Let X be the radioactivity level measured from one of the bottles. What is the optimal decision rule (based on the measurement X) that maximizes the chance of correctly identifying the content of the bottle? (b) What is the associated probability of error?

2. Iocane or Sennam'. An absent-minded chemistry professor forgets to label two identically looking bottles. One contains a chemical named \"Iocane\" and the other contains a chemical named \"Sennari\". It is well known that the radioactivity level of \"Iocane\" has the Unif [0, 1] distribution, While the radioactivity level of \"Sennari\" has the Exp(1) distribution. (a) Let X be the radioactivity level measured from one of the bottles. What is the optimal decision rule (based on the measurement X) that maximizes the chance of correctly identifying the content of the bottle? (b) What is the associated probability of error