Probability | Part IA, 2001

A taxi travels between four villages, W,X,Y,ZW, X, Y, Z, situated at the corners of a rectangle. The four roads connecting the villages follow the sides of the rectangle; the distance from WW to XX and YY to ZZ is 5 miles and from WW to ZZ and YY to X10X 10 miles. After delivering a customer the taxi waits until the next call then goes to pick up the new customer and takes him to his destination. The calls may come from any of the villages with probability 1/41 / 4 and each customer goes to any other village with probability 1/31 / 3. Naturally, when travelling between a pair of adjacent corners of the rectangle, the taxi takes the straight route, otherwise (when it travels from WW to YY or XX to ZZ or vice versa) it does not matter. Distances within a given village are negligible. Let DD be the distance travelled to pick up and deliver a single customer. Find the probabilitites that DD takes each of its possible values. Find the expected value EDE D and the variance Var DD.

Typos? Please submit corrections to this page on GitHub.