Consider this game of chance with a monetary payoff. first, a real number u is chosen uniformly at random from the interval [0, 10s]. next, an integer x is chosen according to the poisson distribution with parameter u. the player receives a reward of $x. what would be the fair price charged for playing this game? that is, how much should it cost to play so that expected net gain is zero?

Two trains leave a station on different tracks. the tracks make an angle of 130°, with the station as a vertex. the first train travels 100 km and makes its first stop at point a, while the second train travels 200 km and makes it first stop at point b. how far apart are the trains when both are at their first stop? round the answer to the nearest integer. a) 65 km b) 139 km c) 224 km d) 275 km