Astatistics professor bought a new car for $35,000. for the next 5 years, she used several automotive web pages to estimate the value of the car. she then found the least-squares regression line for the data to be y 35035.71 - 4142.86x. the correlation coefficient was-0.99. would it be accurate to use this equation to predict the value of the car after 10 years? o no, because that would be extrapolation. o yes, because the correlation is very strong. o no, because the value of cars is unpredictable over time.

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.