We are to distribute n balls randomly into k boxes. What is the expected number of...
We are to distribute n balls randomly into k boxes. What is the expected number of empty boxes and the variance of the number of empty boxes?
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We are to distribute n balls randomly into k boxes.
What is the expected number of...
We randomly distribute 5 identical balls to 3 distinct boxes numbered 1,2,3. Given that no box...
We randomly distribute 5 identical balls to 3 distinct boxes numbered 1,2,3. Given that no box is empty find the probability that box 1 contains 3 balls.
6) Assume that we have n boxes and each one of them contains k white balls...
6) Assume that we have n boxes and each one of them contains k white balls and n-k black balls. We choose a box at random and we choose two balls from it (after choosing the first one we are not allowed to put it back). Compute the probability that both balls are white.
6) Assume that we have n boxes and each one of them contains k white balls...
6) Assume that we have n boxes and each one of them contains k white balls and n-k black balls. We choose a box at random and we choose two balls from it (after choosing the first one we are not allowed to put it back). Compute the probability that both balls are white.
You have N boxes (labeled 1,2,..., N), and you have k balls. You drop the balls...
You have N boxes (labeled 1,2,..., N), and you have k balls. You drop the balls into the boxes, independently of each other. For each ball the probability that it will land in a particular box is 1/N. Let Xi be the number of balls in box 1 and Xv the number of balls in box Ν. Calculate Corr(X1, XN)
5. Three balls are placed at random in three boxes, with no restriction on the number of balls per box. (a) List the 27 equally probable outcomes of this experiment. Be sure to explain your notat...
5. Three balls are placed at random in three boxes, with no restriction on the number of balls per box. (a) List the 27 equally probable outcomes of this experiment. Be sure to explain your notation. (b) Find the probability of each of the following events: A: "the first box is empty" B: "the first two boxes are empty". C: "no box contains more than one ball". (c) Find the probabilities of events A, B and C when three balls...
12) How many ways are there to distribute 150 identical balls to 12 distinct boxes, 6...
12) How many ways are there to distribute 150 identical balls to 12 distinct boxes, 6 red boxes labelled 1 to 6 and 6 blue boxes labelled 1 to 6, such that the blue be with label i and the red box with labeli receive the same number of balls, for every ie (1,2,3,4,5, 6}? [10 marks
12) How many ways are there to distribute 150 identical balls to 12 distinct boxes, 6 red boxes labelled 1 to 6 and...
3. You have N boxes (labeled 1,2,... , N), and you have k balls. You drop...
3. You have N boxes (labeled 1,2,... , N), and you have k balls. You drop the balls into the boxes, independently of each other. For each ball the probability that it will land in a particular box is 1/N. Let Xi be the number of balls in box 1 and XN the number of balls in box N. Calculate Corr(X,XN)
3. You have N boxes (labeled 1,2,..., N), and you have k balls. You drop the...
3. You have N boxes (labeled 1,2,..., N), and you have k balls. You drop the balls into the boxes, independently of each other. For each ball the probability that it will land in a particular box is 1/N. Let Xi be the number of balls in box 1 and Xv the number of ball in bax N. Calculate Com,X)
If n distinct objects are distributed randomly into n distinct boxes, what is the probability that:...
If n distinct objects are distributed randomly into n distinct boxes, what is the probability that: Exactly two boxes are empty?
Two balls are placed randomly into two boxes labeled as I and II. Let X denote the number of balls in box I and Y denote the number of occupied boxes. (a) Find the joint density function of X and Y. (...
Two balls are placed randomly into two boxes labeled as I and II. Let X denote the number of balls in box I and Y denote the number of occupied boxes. (a) Find the joint density function of X and Y. (b) Compute E(X) and the conditional expectation E(X|Y= 1).
6) Assume that we have n boxes and each one of them contains k white balls and n-k black balls. We choose a box at random and we choose two balls from it (after choosing the first one we are not allowed to put it back). Compute the probability that both balls are white.
6) Assume that we have n boxes and each one of them contains k white balls and n-k black balls. We choose a box at random and we choose two balls from it (after choosing the first one we are not allowed to put it back). Compute the probability that both balls are white.
You have N boxes (labeled 1,2,..., N), and you have k balls. You drop the balls into the boxes, independently of each other. For each ball the probability that it will land in a particular box is 1/N. Let Xi be the number of balls in box 1 and Xv the number of balls in box Ν. Calculate Corr(X1, XN)
5. Three balls are placed at random in three boxes, with no restriction on the number of balls per box. (a) List the 27 equally probable outcomes of this experiment. Be sure to explain your notation. (b) Find the probability of each of the following events: A: "the first box is empty" B: "the first two boxes are empty". C: "no box contains more than one ball". (c) Find the probabilities of events A, B and C when three balls...
12) How many ways are there to distribute 150 identical balls to 12 distinct boxes, 6 red boxes labelled 1 to 6 and 6 blue boxes labelled 1 to 6, such that the blue be with label i and the red box with labeli receive the same number of balls, for every ie (1,2,3,4,5, 6}? [10 marks
12) How many ways are there to distribute 150 identical balls to 12 distinct boxes, 6 red boxes labelled 1 to 6 and...
3. You have N boxes (labeled 1,2,... , N), and you have k balls. You drop the balls into the boxes, independently of each other. For each ball the probability that it will land in a particular box is 1/N. Let Xi be the number of balls in box 1 and XN the number of balls in box N. Calculate Corr(X,XN)
3. You have N boxes (labeled 1,2,..., N), and you have k balls. You drop the balls into the boxes, independently of each other. For each ball the probability that it will land in a particular box is 1/N. Let Xi be the number of balls in box 1 and Xv the number of ball in bax N. Calculate Com,X)
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