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

Expert Solution

Please rate. Cheers !!

Y1	Y2	Z (Y1 * Y2)	P (Z)
0	0	0	0.01
1	0	0	0.09
2	0	0	0.09
3	0	0	0.01
0	1	0	0.03
1	1	1	0.27
2	1	2	0.27
3	1	3	0.03
0	2	0	0.01
1	2	2	0.09
2	2	4	0.09
3	2	6	0.01
		SUM	1

Below is the probability distribution of Z (Y1 * Y2)

Z	P (Z)
0	0.24
1	0.27
2	0.36
3	0.03
4	0.09
6	0.01
SUM	1

milcah answered 1 year ago

a box contains two red balls , one white ball and one blue ball. A sample...

a box contains two red balls , one white ball and one blue ball. A sample of two balls was drawn randomly, respectively (without return), If the variable X express the number of white balls and the variable Y express the number of blue balls in the sample, find : A- Fxy(0,1) B- Coefficient of correlation between the two variables and then commented on it

possibility tree One box contains two black balls (labeled B1 and B2) and one white ball....

possibility tree One box contains two black balls (labeled B1 and B2) and one white ball. A second box contains one black ball and two white balls (labeled W1 and W2). Suppose the following experiment is performed: One of the two boxes is chosen at random. Next a ball is randomly chosen from the box. Then a second ball is chosen at random from the same box without replacing the first ball. a. Construct the possibility tree showing all possible...

Following are three boxes containing balls. Box #1 contains 2 black balls and 1 white ball....

Following are three boxes containing balls. Box #1 contains 2 black balls and 1 white ball. Box #2 contains 2 black balls and 2 white balls. Box #3 contains 1 black ball and 2 white ball. Draw a ball from Box 1 and place it in Box 2. Then draw a ball from Box 2 and place it in Box 3. Finally draw a ball from Box 3 . What is the possibility that the last ball drawn, from Box...

An urn contains 7 black balls, 4 red balls, 3 white balls and 1 blue ball,...

An urn contains 7 black balls, 4 red balls, 3 white balls and 1 blue ball, and a player is to draw one ball. If it is black, he wins $1, if it is red, he wins $2, if it is white he wins $3 and if it is blue, he pay $25. a. Set up the empirical probability distribution for the random variable X, the payoff of the game. Game Payoff (X) Probability [P(X) $1 $2 $3 $4 b....

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.

A box contains 7 black balls and a single red ball. Peter and Frances draw without...

A box contains 7 black balls and a single red ball. Peter and Frances draw without replacement balls from this urn, alternating after each draw until the red ball is drawn. The game is won by the player who happens to draw the single red ball. Peter is a gentleman and offers Frances the choice of whether she wants to start or not. Frances has a hunch that she might be better off if she starts; after all, she might...

A box contains one yellow, two red, and three green balls. Two balls are randomly chosen...

A box contains one yellow, two red, and three green balls. Two balls are randomly chosen without replacement. Define the following events, and use them to find the conditional probabilities below. A:{A:{ One of the balls is yellow }} B:{B:{ At least one ball is red }} C:{C:{ Both balls are green }} D:{D:{ Both balls are of the same color }} a) P(B¯¯¯¯|A)= b) P(B¯¯¯¯|D)= c) P(C|D)= Suppose that E and F are events in the sample space with...

Box 1 contains 3 red balls, 5 green balls and 2 white balls. Box 2 contains...

Box 1 contains 3 red balls, 5 green balls and 2 white balls. Box 2 contains 5 red balls, 3 green balls and 1 white ball. One ball of unknown color is transferred from Box 1 to Box 2. (a) What is the probability that a ball drawn at random from Box 2 is green? (b) What is the probability that a ball drawn from Box 1 is not white?

3. A box contains 5 red balls, 3 blue balls and 1 black balls. Take two...

3. A box contains 5 red balls, 3 blue balls and 1 black balls. Take two balls out randomly. Let X be number of red balls and Y be the number of black balls. (1) Find the joint distribution of (X, Y ). (2) Find P(X = 1|Y = 1).

A box contains 2 ?red, 3 white and 3 green balls. Two balls are drawn out...

A box contains 2 ?red, 3 white and 3 green balls. Two balls are drawn out of the box in succession without replacement. What is the probability that both balls are the same? color?

Question