3. You have N boxes (labeled 1,2,..., N), and you have k balls. You drop the...
You have N boxes (labeled 1,2,..., N), and you have k balls. You drop the balls into the boxes, independently of each other. For each ball the probability that it will land in a particular box is 1/N. Let Xi be the number of balls in box 1 and Xv the number of balls in box Ν. Calculate Corr(X1, XN)
3. You have N boxes (labeled 1,2,... , N), and you have k balls. You drop the balls into the boxes, independently of each other. For each ball the probability that it will land in a particular box is 1/N. Let Xi be the number of balls in box 1 and XN the number of balls in box N. Calculate Corr(X,XN)
boxes, n 2, and for each k E {1,...,n} the k-th box contains k watches. In We have every box each watch is defective with probability independently of the other watches in the box. We choose a box randomly. Given that there are no defective watches in it compute the probability that this was the second box boxes, n 2, and for each k E {1,...,n} the k-th box contains k watches. In We have every box each watch is...
A box contains 5 Balls labeled with the number "1", 3 balls labeled with the number "2", and 1 ball labeled with the number "3". Two balls are selected, without replacement. Let X be the total of the values on the two balls. Find the mean of X.
6) Assume that we have n boxes and each one of them contains k white balls and n-k black balls. We choose a box at random and we choose two balls from it (after choosing the first one we are not allowed to put it back). Compute the probability that both balls are white.
6) Assume that we have n boxes and each one of them contains k white balls and n-k black balls. We choose a box at random and we choose two balls from it (after choosing the first one we are not allowed to put it back). Compute the probability that both balls are white.
. There are two boxes with red and blue balls in them. Box I has 1 red and 4 blue balls; Box II has 3 red and 2 blue balls. There is a fair coin with Box I written on one side and Box II written on the other. You toss the coin and then draw 2 balls without replacement out of the box that comes up on the face of the coin. a. Let Y be the number of...
There are two boxes with red and blue balls in them. Box I has 1 red and 4 blue balls; Box II has 3 red and 2 blue balls. There is a fair coin with Box I written on one side and Box II written on the other. You toss the coin and then draw 2 balls without replacement out of the box that comes up on the face of the coin. a. Let Y be the number of red...
5. Three balls are placed at random in three boxes, with no restriction on the number of balls per box. (a) List the 27 equally probable outcomes of this experiment. Be sure to explain your notation. (b) Find the probability of each of the following events: A: "the first box is empty" B: "the first two boxes are empty". C: "no box contains more than one ball". (c) Find the probabilities of events A, B and C when three balls...
b) You have three boxes. In the first box, there are 4 white balls and 2 red balls. In the second box, there are only 10 red balls and in the third box, there are 10 red balls and 5 white balls. A red ball is extracted blindly from a box chosen at random, but you don’t know from which box the ball was extracted What is the probability that the first box was chosen? What is the probability that...