Question: In an urn containing n balls the ith ball has
In an urn containing n balls, the ith ball has weight W(i), i = 1, . . . , n. The balls are removed without replacement, one at a time, according to the following rule: At each selection, the probability that a given ball in the urn is chosen is equal to its weight divided by the sum of the weights remaining in the urn. For instance, if at some time i1, . . . , ir is the set of balls remaining in the urn, then the next selection will be ij with probability
Compute the expected number of balls that are withdrawn before ball number 1 is removed.
Answer to relevant QuestionsFor a group of 100 people, compute (a) The expected number of days of the year that are birthdays of exactly 3 people: (b) The expected number of distinct birthdays. If 101 items are distributed among 10 boxes, then at least one of the boxes must contain more than 10 items. Use the probabilistic method to prove this result. If E[X] = 1 and Var(X) = 5, find (a) E[(2 + X)2]; (b) Var(4 + 3X). The joint density function of X and Y is given by f(x, y) = 1/ye−(y+x/y), x > 0, y > 0 Find E[X], E[Y], and show that Cov(X, Y) = 1. There are two misshapen coins in a box; their probabilities for landing on heads when they are flipped are, respectively, .4 and .7. One of the coins is to be randomly chosen and flipped 10 times. Given that two of the first ...
Post your question