Charlotte owns two entertainment websites. Here are some details about those websites for one entire month: Website A Website B Number of writers 555 111111 Number of posts posted 110110110 200200200 Average number of words of post 100100100 170170170 Average likes per post 350035003500 350035003500 Average comments per post 500500500 450450450 Number of new subscribers 900090009000 20{,}00020,00020, comma, 000 Revenue \$30{,}000$30,000dollar sign, 30, comma, 000 \$75{,}000$75,000dollar sign, 75, comma, 000 Expenses \$20{,}000$20,000dollar sign, 20, comma, 000 \$47{,}000$47,000dollar sign, 47, comma, 000 Profit (Revenue-−minusExpenses) \$10{,}000$10,000dollar sign, 10, comma, 000 \$28{,}000$28,000dollar sign, 28, comma, 000 Charlotte wants to know which website produces a larger amount of content per a single writer. 1) Charlotte thought of two different ways to define this quantity. Identify these two definitions among the following options.

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.