Accident investigators can estimate the speed of a vehicle involved in a crash by examining the skid marks left by the tires on the pavement. The algebraic relationship is shown by the formula
V30fd with s representing the speed in miles per hour and d representing the skid distance in
feet. The value f is determined by the friction of the pavement: wet concrete is much more slippery
than hot asphalt. A typical value for f, assuming a dry roadway, is 0.7. After a minor car accident on a
dry day, Charlie insisted to his parents that he wasn't exceeding the 35 mph speed limit. An accident
investigator found that the skid marks left by Charlie's tires were 75 feet long. Does the investigator's
skid analysis indicate Charlie was telling the truth

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.