Who Has Which Jobs? Because of the high cost of living, Kimberly, Terry, and Oscar each holds down
two jobs, but no two have the same occupation. The occupations are doctor,
engineer, teacher, lawyer, writer, and painter. Given the following
information, determine the occupations of each individual.
The doctor had lunch with the teacher.
The teacher and the writer went fishing with Kimberly.
The painter is related to the engineer.
The doctor hired the painter to do a job.
Terry lives next door to the writer.
Oscar beat Terry and the painter at tennis.
Oscar is not the doctor.
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I’m

Aprisoner is trapped in a cell containing three doors. the first door leads to a tunnel that returns him to his cell after two days of travel. the second leads to a tunnel that returns him to his cell after three days of travel. the third door leads immediately to freedom. (a) assuming that the prisoner will always select doors 1, 2 and 3 with probabili- ties 0.5,0.3,0.2 (respectively), what is the expected number of days until he reaches freedom? (b) assuming that the prisoner is always equally likely to choose among those doors that he has not used, what is the expected number of days until he reaches freedom? (in this version, if the prisoner initially tries door 1, for example, then when he returns to the cell, he will now select only from doors 2 and 3.) (c) for parts (a) and (b), find the variance of the number of days until the prisoner reaches freedom. hint for part (b): define ni to be the number of additional days the prisoner spends after initially choosing door i and returning to his cell.