Apublic opinion researcher has a budget of $20,000 for taking a survey. she knows that 90% of all households have telephones. telephone interviews cost $10 per household; in-person interviews cost $30 each if all interviews are conducted in person, and $40 each if only nonphone households are interviewed in person (because there will be extra travel costs). assume that the variances in the phone and nonphone groups are similar, and that the fixed costs are co $5000. how many households should be interviewed in each group if a all househol ds are interviewed in person households with a phone are contacted by telephone and households without a phone are contacted in person. b

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.