6) Assume that we have n boxes and each one of them contains k white balls...
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.
5) Box 1 contains w white balls and b black balls. Box 2 contains w white balls and b black balls. We take one ball from Box 1 and place it into Box 2. Then we take a ball from Box 2 and place it into Box 1. Finally we take a ball from Box 1. Compute the probability that this ball is black 6) Assume that we have n boxes and each one of them contains k white balls...
Problem 2. We have 2 boxes, each containing 3 balls. Box number 1 contains one black and two white balls; box nber 2 contains two black and one white ba Our friend chooses one of the boxes at random, probability of choosing box number 1 is p. Then he takes one bal from a chosen box (each of three balls can be taken chosen equally likely), and it turns out to be white We are going to find MAP estimate...
We have 2 boxes, each containing 3 balls. Box number 1 contains one black and two white balls; box number 2 contains two black and one white ball. Our friend chooses one of the boxes at random, probability of choosing box number 1 is p. Then he takes one ball from a chosen box (each of three balls can be taken chosen equally likely), and it turns out to be white. We are going to find MAP estimate for the...
There are 3 black and 4 white balls in a box. One ball is taken out at random. If it is black, then two white balls are put back in the box. If it is white, then one black ball is put back in the box. After that procedure another ball is taken out of the box. What is the probability that the first ball taken was white is the second ball taken was white?
2(15)(a) An urn contains 4 white and 4 black balls. We randomly choose 4 balls. If 2 of them are white and 2 are black, we stop. If not, we replace the balls in the urn and again randomly select 4 balls. This continues until exactly 2 of the 4 chosen are white. What is the probability that we shall maken selections? (b)Compute E[x2] for a Poisson random variable X.
An urn contains M white and N black balls. Balls are randomly selected, one at a time, until a black one is obtained. If we assume that each ball selected is replaced before the next one is drawn, what is the probability that a) exactly x draws are needed? b) at least k draws are needed?
B2. An urn contains k black balls and N -k white balls, with N known and k unknown. n balls are selected at random without replacement from the box. Construct a statistical model and use your statistic model to estimate k using the method-of-moments. Hint: Construct a statistical model such that the sample size is 1.
5) Box 1 contains wi white balls and bi black balls. Box 2 contains w2 white balls and b2 black balls. We take one ball from Box 1 and place it into Box 2. Then we take a ball from Box 2 and place it into Box 1. Finally we take a ball from Box 1. Compute the probability that this ball is black.
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...