A box contains three balls labeled 0, 1, and 2. A ball is chosen at random and then a coin is flipped that number of times. Let: X=the number on the ball Y =the number of heads obtained
(a) Give the joint PMF of X and Y.
(b) What is the probability the sum of X and Y is at least 2?
A box contains three balls labeled 0, 1, and 2. A ball is chosen at random...
Please provide the function as well. Urn A contains three balls labeled from 1 to 3 and urn B contains 2 balls labeled from 1 to 2. A ball is randomly selected from urn A and another ball is randomly selected from urn B. Find the joint probability mass function of X and Y when (a) X is the largest value obtained on the selected balls and Y is the sum of the values; (b) X is the value on...
A box contains four green balls. We choose balls at random, with replacement, according to the following rules: (i) Upon choosing each ball from the box, we mark it with a red stripe before replacing it in the box. (ii) We stop as soon as we choose a ball with a red stripe (i.e. the ball has been chosen twice). Let x= the number of times that balls were chosen from the box. (Note that x must be at least...
A box contains 5 green balls. We choose balls at random, with replacement, according to the following rules: (i) Upon choosing each ball from the box, we mark it with a red stripe before replacing it in the box. (ii) We stop as soon as we choose a ball with a red stripe (i.e. the ball has been chosen twice). Let x= the number of times that balls were chosen from the box. (Note that x must be at least...
2. A box contains 4 white and 6 black balls. A random sample of size 4 is chosen. Let X denote the number of white balls in the sample. An additional ball is now selected from the remaining 6 balls in the box. Let Y equal 1 if this ball is white and 0 if it is black. Find (a) Var(Y|X=0). (b) Var(X)Y= 1).
A ball is taken at random from an urn containing 2 red balls and 3 blue balls. If the ball is red a fair coin is tossed three times. If the ball is blue non-fair coin is tossed three times; for this second coin the probability of heads is .6. In either case we count the number of heads in the three tosses and call that number X. (a) Compute the conditional probability that X-2 if it is known that...
A box contains 5 Balls labeled with the number "1", 3 balls labeled with the number "2", and 1 ball labeled with the number "3". Two balls are selected, without replacement. Let X be the total of the values on the two balls. Find the mean of X.
Problem 3. A ball is taken at random from an urn containing 2 red balls and 3 blue balls. If the ball is red a fair coin is tossed three times. If the ball is blue non-fair coin is tossed three times; for this second coin the probability of heads is .6. In either case we count the number of heads in the three tosses and call that number X (a) Compute the conditional probability that X-2 if it is...
IA Box 1 contains 5 red and 4 green balls and box 2 contains 4 red and 6 green balls. Three balls are randomly drawn from box 1 and placed in box 2. Then a ball is taken from box 2. If the ball taken from box 2 is found red, find the probability that 2 red and 1 green balls are transferred from box 1 to box 2? IB. Two coins Ci and C2 have a probability of falling...
A box contains seven red balls and five black balls. Three balls are selected at random from the box. Compute the probability that (d) at least one ball is red.
The number of balls in a box, N, is a Poisson variable with rate A. Each ball in the box can be white with probability p or red, with probability q = 1-p. Let X be the number of white balls in a box and Y the number of red balls in the same box, so that X+Y = N. The joint probability P(X i, Y = j), i, j 0? (b (A)
The number of balls in a box,...