Homework Answers
At first we will consider both problem separately and then we will calculate the required probabilities for each problem and get our required results...
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2. A box contains 4 white and 6 black balls. A random sample of size 4...
Box 1 contains a red balls and b white balls. Box 2 contains c red balls...
Box 1 contains a red balls and b white balls. Box 2 contains c red balls and d white balls. One ball is randomly drawn from Box 1 and put into Box 2, and then one ball is randomly drawn from Box 2 and put back in Box 1. Finally, one ball is drawn at random again from Box 2. Let X denote the number of red balls drawn from Box 2 the 2nd time. Write down the distribution of...
5) Box 1 contains w white balls and b black balls. Box 2 contains w 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...
2. A box contains 5 red balls, 7 white balls, and 8 black balls. Four balls...
2. A box contains 5 red balls, 7 white balls, and 8 black balls. Four balls are randomly chosen (without replace- ment). What is the probability that (a) 1 red ball, 2 white balls, and 1 black ball are chosen? (b) exactly two red balls are chosen? (c) the first chosen is black, the last three chosen are two white balls and one black ball?
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...
5) Box 1 contains wi white balls and bi black balls. Box 2 contains w2 white...
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.
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...
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 ran...
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...
5) Box 1 contains w white balls and b black balls. Box 2 contais white balls...
5) Box 1 contains w white balls and b black balls. Box 2 contais 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.
An urn contains 7 white balls and 3 black balls. Two balls are selected at random...
An urn contains 7 white balls and 3 black balls. Two balls are selected at random without replacement. What is the probability :1 The first ball is black and the second ball is white.? 2: One ball is white and the other is black? 3:the two 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...
2. A box contains 5 red balls, 7 white balls, and 8 black balls. Four balls are randomly chosen (without replace- ment). What is the probability that (a) 1 red ball, 2 white balls, and 1 black ball are chosen? (b) exactly two red balls are chosen? (c) the first chosen is black, the last three chosen are two white balls and one black ball?
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...
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.
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...
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...
5) Box 1 contains w white balls and b black balls. Box 2 contais 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.
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