L. An un contains n red balls and n black balls. Balls are drawn sequentially from...
Suppose we have two urns (a left urn and a right urn). The left urn contains N black balls and the right urn contains N red balls. Every time step you take one ball (chosen randomly) from each urn, swap the balls, and place them back in the urns. Let Xm be the number of black balls in the left urn after m time steps. Find the Markov chain model and find the unique stationary distribution when N=5
Urn one contains two red, one black balls, urn two contains one red, three black balls, and urn three contains one red, one black balls. A student chooses urn one or urn two at random, and selects one ball from the chosen urn at random and transfers it into urn three. Then he draws a ball from urn three. Given that the ball he draws is red, what is the probability that the transferred ball is red?
An urn contains 7 white, 3 red and 10 black balls. If five balls are drawn at random, find the probability that at least one red ball is selected.
Problem#1(40 Points) An urn contains two balls, one is red and one is black. A ball is drawn at random and its color is noted then returned back to the urn. This process is repeated, and stoped when the red ball is drawn or until a maximum of 6 trials. Let the random variable X denotes the number of trials. 1. Find the p.m.fof X. (10 Points)
an urn contains n red and n blue balls. Balls are drawn at random (without replacement) in stages until one color is depleted. The number of draws until this event happens is called waiting time. what is the distribution of this waiting time?
An urn initially contains r red balls and s black balls. A ball is selected at random but not removed and a balls of the same color as the selection are added to the urn. The process is then repeated with a balls of one color or the other added to the urn at each epoch. With each addition the population of the urn increases by a and it is helpful to imagine that the (a) What is the probability...
Question 3. (exercise 3.11-13 in textbook) An urn contains r red balls and b blue balls. A ball is chosen at random from the urn, its color is noted, and it is returned together with d more balls of the same color. This is repeated indefinitely. What is the probability that (a) The second ball drawn is blue? (b) The first ball drawn is blue given that the second ball drawn is blue? (c) Let Bn denote the event that...
Question 3. (exercise 3.11-13 in textbook) An urn contains r red balls and b blue balls. A ball is chosen at random from the urn, its color is noted, and it is returned together with d more balls of the same color. This is repeated indefinitely. What is the probability that (a) The second ball drawn is blue? (b) The first ball drawn is blue given that the second ball drawn is blue? (c) Let Bn denote the event that...
Urn A contains 5 green and 3 red balls, and urn B contains 2 green and 6 red balls. One ball is drawn from urn A and transferred to Urn b. Then one ball is drawn from urn B and transferred to urn A. Let X=the number of green balls in urn A after this process. List the possible values for X and then find the entire probability distribution for X.
8) For Polya's urn model with r red balls, b black balls and parameters cE N (the number of extra balls we insert every time) and n EN,n 2 3 (the number of times we perform the a) Show that the probability that the k-th chosen ball (k e (1,...,n]) is red is equal to b) Given that the second chosen ball was red compute the probability that the first one experiment), do the following: was red as well.