Consider n independent rolls of a k-sided fair die with k 2: the sides of the die are labelled 1; 2; : : : ; k and each side has probability 1=k of facing up after a roll. Let the random variable Xi denote the number of rolls that result in side i facing up. The joint p. m.f. of X1; : : : ;Xk is multinomial. (The multinomial distribution was discussed in problem 3 of recitation 4.)

Which expression is equivalent to 5r674 pression is equivalent to see lo 5r614) 4r322,4 ) 5 ( 2 5t5 |

Four airplanes carrying a total of 400 passengersarrive at the detroit airport. the airplanes carry, respectively,50, 80, 110, and 160 passengers. a) one of the 400 passengers is selected uniformly at random. let x denote the number of passengers that were on theairplane carrying the randomly selected passenger. find var(x)for x as given in the problemb) one of the 4 airplane drivers is also selected uniformly atrandom. let y denote the number of passengers on the chosen driver’s airplane. find var(y) for y as given in the problem

The multiplicative property of equality states that for real numbers a, b, c, and d, if a = b and c = d, then ac = bd. true false