Medical students compared two types of knee surgery to determine if patients were able to return to their active lifestyles. They studied partial knee replacement and total knee replacement. Identify the response and explanatory variables. The response variable is the type of knee surgery, and the explanatory variable is the amount of activity the patients were able to do after surgery.
The response variable is total knee replacement, and the explanatory variable is partial knee replacement.
The response variable is partial knee replacement, and the explanatory variable is the amount of activity the patients were able to do after surgery.
The response variable is the amount of activity the patients were able to do after surgery, and the explanatory variable is the type of knee surgery.
The response variable is partial knee replacement, and the explanatory variable is total knee replacement.

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.