Question
In: Statistics and Probability
Three white and three black balls are distributed in two urns in such a way that...
Three white and three black balls are distributed in two urns in such a way that each contains three balls. We say that the system is in state i,i = 0, 1, 2, 3, if the first urn contains i white balls. At each step, we draw one ball from each ufn and place the ball drawn from the first urn into the second, and conversely with the ball from the second urn. Let Xq denote the state of the system after the Cth step. Explain why (X,. n 0, 1. 2. ...) is a Markov chain and calculate its transition probability matrix.
Solutions
orchestra answered 2 years agoRelated Solutions
Three white and three black balls are distributed in two urns in such a way that...
Three white and three black balls are distributed in two urns in
such a way that each contains three balls. We will say that the
system is in state i, i = 0, 1, 2, 3, if the first urn contains i,
white balls. At each step, we draw one ball from each urn – the
ball drawn from the first urn is placed into the second, and the
ball from the second urn is placed into the first. Let...
There are three urns each containing seven red, five green, and three white balls, and two...
There are three urns each containing seven red, five green, and
three white balls, and two old urns each containing five red, three
green, and seven white balls. The urns are identical except for an
old or new date stamped beneath the base. If a single red ball is
randomly drawn from one of these urns, was it most probably drawn
from an old urn or a new urn?
A box contains three white balls, two black balls, and one red ball. Three balls are...
A box contains three white balls, two black balls, and one red
ball. Three balls are drawn at random without replacement. Let Y1
be the number of white balls drawn, and Y2 the number of black
balls drawn. Find the distribution of Z = Y1 × Y2
Urn A contains four white balls and three black balls. Urn B contains six white balls...
Urn A contains four white balls and three black balls. Urn B
contains six white balls and seven black balls. A ball is drawn
from Urn A and then transferred to Urn B. A ball is then drawn from
Urn B. What is the probability that the transferred ball was white
given that the second ball drawn was white? (Round your answer to
three decimal places.)
I can't seem to figure this out! Please help! Thank you!
There are two urns, urn I and urn II. Urn I contains 2 white balls and...
There are two urns, urn I and urn II. Urn I contains 2 white
balls and 4 red balls, and urn II
contains 1 white ball and 1 red ball. A ball is randomly chosen
from urn I and put into urn II,
and a ball is then randomly selected from urn II. What is the
probability that the ball selected
from urn II is white?
Suppose that there is a white urn containing two white balls and three red balls and...
Suppose that there is a white urn containing two white balls and
three red balls and there is a red urn containing two white balls
and four red balls. An experiment consists of selecting at random a
ball from the white urn and then (without replacing the first
ball) selecting at random a ball from the urn having the color of
the first ball. Find the probability that the second ball is
red.
An urn contains six white balls and four black balls. Two balls are randomly selected from...
An urn contains six white balls and four black balls. Two balls
are randomly selected from the urn. Let X represent the
number of black balls selected.
(a) Identify the probability distribution of X. State
the values of the parameters corresponding to this
distribution.
(b) Compute P(X = 0), P(X =
1), and P(X = 2).
(c) Consider a game of chance where you randomly select two
balls from the urn. You then win $2 for every black ball selected...
An urn contains two white and two black balls. A ball is drawn at random. If...
An urn contains two white and two black balls. A ball is drawn
at random. If it is white, it is not replaced into the urn,
otherwise it is replaced with another ball of the same color. The
process is repeated. Find the probability that the third ball drawn
is black.
There are 2 white balls, 9 black balls and 29 green balls in a box. We...
There are 2 white balls, 9 black balls and 29 green balls in a
box. We draw a ball twice, without replacement. Let X and Y denote
the number of white and black balls, respectively, among the drawn.
Calculate Cov(X,Y).
1). Given a container with 6 white balls and 9 black balls, if 4 balls are...
1). Given a container with 6 white balls and 9 black balls, if 4
balls are chosen randomly, what is the probability that exactly two
are white?
2). Given a container with 6 white balls and 9 black balls, if 4
balls are chosen randomly, and one of the chosen balls is black,
what is the probability that exactly two are white?
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