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2, Five white balls and five black balls are distributed in two urns in such a...
Five white balls and two red balls are distributed between two urns A and B in...
Five white balls and two red balls are distributed between two urns A and B in such a way that urn A contains 2 white balls and 2 red balls and urn B contains 3 white balls. At each step, we draw one ball from each urn and place the ball drawn from urn A into urn B and conversely with the ball from urn B. Find the long run proportion of time that urn A will contain 4 white...
5. (15 points) Four blue and four maize balls are distributed in two urns in such...
5. (15 points) Four blue and four maize balls are distributed in two urns in such a way that each contains four balls. We say that the systern is in state i, i = (), 1, 2, 3, 4, if the first urn contains i maize balls. At each step, we draw one ba from each urn and place the ball drawn from the first urn into the second, and conversely with the ball from the second urn. Let Xn...
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.
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
3. Suppose there are 2 urns such that the first urn contains a white balls and...
3. Suppose there are 2 urns such that the first urn contains a
white balls and b black balls and the second urn contains c white
balls and d black balls. Flip a coin whose probability of landing
heads is p and select a ball from the first urn if the outcome is
heads and from the second if the outcome is tails. What is a value
for p for which the probability that the outcome was heads given
that...
Consider 2 urns. Urn 1 has 2 White Balls and 1 Black Ball. Urn 2 has...
Consider 2 urns. Urn 1 has 2 White Balls and 1 Black Ball. Urn 2 has 1 White Ball and 2 Black Balls. Suppose that one ball is randomly drawn from Urn 1 and put into Urn 2. Then balls are selected one at a time without replacement from Urn 2 until a White Ball is obtained. Let Y be the number of balls drawn from Urn 2 until a white ball is drawn. Find the pdf of Y and...
Example. 2 urns. Red urn contains 3 red balls, 2 white balls. White urn contains 1...
Example. 2 urns. Red urn contains 3 red balls, 2 white balls. White urn contains 1 red ball, 4 white balls. Pick an urn randomly. Randomly select a ball from that urn. Without replacing the 1st ball, select a ball from the urn whose color matches the first ball. Q. Make a tree diagram, complete with probabilities describing this situation. Q. Find the probability that the first ball is white. Q. Find the probability that the second ball is white....
A total of 5 balls of two possible colours, black and white, have been put into...
A total of 5 balls of two possible colours, black and white, have been put into a box. A ball is chosen uniformly at random. If the ball is black, we replace this ball in the box with a white ball. Similarly, if the ball chosen is white, we replace this ball in the box with a black one. Let {Xn,n 2 0) denote the number of white balls in the box after the n-th trial. This defines a Markov...
A total of 5 balls of two possible colours, black and white, have been put into...
A total of 5 balls of two possible colours, black and white, have been put into a box. A ball is chosen uniformly at random. If the ball is black, we replace this ball in the box with a white ball. Similarly, if the ball chosen is white, we replace this ball in the box with a black one. Let {Xn,n 2 0) denote the number of white balls in the box after the n-th trial. This defines a Markov...
2. An urn contains six white balls and four black balls. Two balls are randomly selected...
2. 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 and...
7. An urn contains four black and eight white balls. A sample of five balls is...
7. An urn contains four black and eight white balls. A sample of five balls is selected from the urn repeatedly, each time with replacement of the selected balls (thus restoring the urn to its original state). Let E be the event that the selected sample contains at most two white balls. (a) Find the probability of E (b) What is the expected number of selections until E happens? Name the random variable used. (c) What is the probability that...
5. (15 points) Four blue and four maize balls are distributed in two urns in such a way that each contains four balls. We say that the systern is in state i, i = (), 1, 2, 3, 4, if the first urn contains i maize balls. At each step, we draw one ba from each urn and place the ball drawn from the first urn into the second, and conversely with the ball from the second urn. Let Xn...
3. Suppose there are 2 urns such that the first urn contains a
white balls and b black balls and the second urn contains c white
balls and d black balls. Flip a coin whose probability of landing
heads is p and select a ball from the first urn if the outcome is
heads and from the second if the outcome is tails. What is a value
for p for which the probability that the outcome was heads given
that...
Example. 2 urns. Red urn contains 3 red balls, 2 white balls. White urn contains 1 red ball, 4 white balls. Pick an urn randomly. Randomly select a ball from that urn. Without replacing the 1st ball, select a ball from the urn whose color matches the first ball. Q. Make a tree diagram, complete with probabilities describing this situation. Q. Find the probability that the first ball is white. Q. Find the probability that the second ball is white....
A total of 5 balls of two possible colours, black and white, have been put into a box. A ball is chosen uniformly at random. If the ball is black, we replace this ball in the box with a white ball. Similarly, if the ball chosen is white, we replace this ball in the box with a black one. Let {Xn,n 2 0) denote the number of white balls in the box after the n-th trial. This defines a Markov...
A total of 5 balls of two possible colours, black and white, have been put into a box. A ball is chosen uniformly at random. If the ball is black, we replace this ball in the box with a white ball. Similarly, if the ball chosen is white, we replace this ball in the box with a black one. Let {Xn,n 2 0) denote the number of white balls in the box after the n-th trial. This defines a Markov...
2. 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 and...
7. An urn contains four black and eight white balls. A sample of five balls is selected from the urn repeatedly, each time with replacement of the selected balls (thus restoring the urn to its original state). Let E be the event that the selected sample contains at most two white balls. (a) Find the probability of E (b) What is the expected number of selections until E happens? Name the random variable used. (c) What is the probability that...
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