A box contains 3 marbles: 1 red, 1 green, and 1 blue. Consider an experiment that consists of taking 1 marble from the box and then replacing it in the box and drawing a second marble from the box. Describe the sample space . Repeat when the second marble is drawn without replacing the first marble.

Question

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Answer 1

Textbook Question

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Chapter 2, Problem 2.1P

A box contains 3 marbles: 1 red, 1 green, and 1 blue. Consider an experiment that consists of taking 1 marble from the box and then replacing it in the box and drawing a second marble from the box. Describe the sample space. Repeat when the second marble is drawn without replacing the first marble.

Expert Solution & Answer

To determine

To find: The sample space of given experiment with replacement and without

replacement.

Answer to Problem 2.1P

The sample space with replacement

={(R,R),(R,G),(R,B),(G,G),(G,R),(G,B),(B.,B),(B,R),(B,G)}

The sample space without replacement ={(R,G),(R,B),(G,R),(G,B),(B,R),(B,G)}

Explanation of Solution

Given information:

Consider box contains three marbles. They are 1 Red marble (R) , 1 Green marble (G) , 1

Blue marble (B) .

Calculation:

Sample space is the set of all possible outcomes of a random experiment.

Consider the experiment of drawing two marbles one after another with replacement.

Total number of outcomes =32

Then, the sample space is given by

={(R,R),(R,G),(R,B),(G,G),(G,R),(G,B),(B.,B),(B,R),(B,G)}

Consider the experiment of drawing two marbles one after another without replacement.

Total number of outcomes =3×2=6

Then, the sample space is given by ={(R,G),(R,B),(G,R),(G,B),(B,R),(B,G)}

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5 of 5 (i) Let a discrete sample space be given by Ω = {ω1, 2, 3, 4}, Total marks 12 and let a probability measure P on be given by P(w1) 0.2, P(w2) = 0.2, P(w3) = 0.5, P(w4) = 0.1. = Consider the random variables X1, X2 → R defined by X₁(w3) = 1, X₁(4) = 1, X₁(w₁) = 1, X₁(w2) = 2, X2(w1) = 2, X2(w2) = 2, X2(W3) = 1, X2(w4) = 2. Find the joint distribution of X1, X2. (ii) [4 Marks] Let Y, Z be random variables on a probability space (N, F, P). Let the random vector (Y, Z) take on values in the set [0,1] × [0,2] and let the joint distribution of Y, Z on [0,1] × [0,2] be given by 1 dPy,z(y, z) (y²z + y²²) dy dz. Find the distribution Py of the random variable Y. [8 Marks]

Total marks 16 5. Let (,,P) be a probability space and let X : → R be a random variable whose probability density function is given by f(x) = }}|x|e¯|×| for x Є R. (i) (ii) Find the characteristic function of the random variable X. [8 Marks] Using the result of (i), calculate the first two moments of the random variable X, i.e., E(X") for n = 1, 2. (iii) What is the variance of X? [6 Marks] [2 Marks]

Total marks 16 5. Let (N,F,P) be a probability space and let X : N → R be a random variable such that the probability density function is given by f(x)=ex for x € R. (i) Find the characteristic function of the random variable X. [8 Marks] (ii) Using the result of (i), calculate the first two moments of the random variable X, i.e., E(X") for n = 1,2. (iii) What is the variance of X. [6 Marks] [2 Marks]

Answer 2

Textbook Question

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Chapter 2, Problem 2.1P

A box contains 3 marbles: 1 red, 1 green, and 1 blue. Consider an experiment that consists of taking 1 marble from the box and then replacing it in the box and drawing a second marble from the box. Describe the sample space. Repeat when the second marble is drawn without replacing the first marble.

Expert Solution & Answer

To determine

To find: The sample space of given experiment with replacement and without

replacement.

Answer to Problem 2.1P

The sample space with replacement

={(R,R),(R,G),(R,B),(G,G),(G,R),(G,B),(B.,B),(B,R),(B,G)}

The sample space without replacement ={(R,G),(R,B),(G,R),(G,B),(B,R),(B,G)}

Explanation of Solution

Given information:

Consider box contains three marbles. They are 1 Red marble (R) , 1 Green marble (G) , 1

Blue marble (B) .

Calculation:

Sample space is the set of all possible outcomes of a random experiment.

Consider the experiment of drawing two marbles one after another with replacement.

Total number of outcomes =32

Then, the sample space is given by

={(R,R),(R,G),(R,B),(G,G),(G,R),(G,B),(B.,B),(B,R),(B,G)}

Consider the experiment of drawing two marbles one after another without replacement.

Total number of outcomes =3×2=6

Then, the sample space is given by ={(R,G),(R,B),(G,R),(G,B),(B,R),(B,G)}

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Answer 3

Textbook Question

100%

Chapter 2, Problem 2.1P

A box contains 3 marbles: 1 red, 1 green, and 1 blue. Consider an experiment that consists of taking 1 marble from the box and then replacing it in the box and drawing a second marble from the box. Describe the sample space. Repeat when the second marble is drawn without replacing the first marble.

Expert Solution & Answer

To determine

To find: The sample space of given experiment with replacement and without

replacement.

Answer to Problem 2.1P

The sample space with replacement

={(R,R),(R,G),(R,B),(G,G),(G,R),(G,B),(B.,B),(B,R),(B,G)}

The sample space without replacement ={(R,G),(R,B),(G,R),(G,B),(B,R),(B,G)}

Explanation of Solution

Given information:

Consider box contains three marbles. They are 1 Red marble (R) , 1 Green marble (G) , 1

Blue marble (B) .

Calculation:

Sample space is the set of all possible outcomes of a random experiment.

Consider the experiment of drawing two marbles one after another with replacement.

Total number of outcomes =32

Then, the sample space is given by

={(R,R),(R,G),(R,B),(G,G),(G,R),(G,B),(B.,B),(B,R),(B,G)}

Consider the experiment of drawing two marbles one after another without replacement.

Total number of outcomes =3×2=6

Then, the sample space is given by ={(R,G),(R,B),(G,R),(G,B),(B,R),(B,G)}

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02:21

Answer 4

Textbook Question

100%

Chapter 2, Problem 2.1P

A box contains 3 marbles: 1 red, 1 green, and 1 blue. Consider an experiment that consists of taking 1 marble from the box and then replacing it in the box and drawing a second marble from the box. Describe the sample space. Repeat when the second marble is drawn without replacing the first marble.

Expert Solution & Answer

To determine

To find: The sample space of given experiment with replacement and without

replacement.

Answer to Problem 2.1P

The sample space with replacement

={(R,R),(R,G),(R,B),(G,G),(G,R),(G,B),(B.,B),(B,R),(B,G)}

The sample space without replacement ={(R,G),(R,B),(G,R),(G,B),(B,R),(B,G)}

Explanation of Solution

Given information:

Consider box contains three marbles. They are 1 Red marble (R) , 1 Green marble (G) , 1

Blue marble (B) .

Calculation:

Sample space is the set of all possible outcomes of a random experiment.

Consider the experiment of drawing two marbles one after another with replacement.

Total number of outcomes =32

Then, the sample space is given by

={(R,R),(R,G),(R,B),(G,G),(G,R),(G,B),(B.,B),(B,R),(B,G)}

Consider the experiment of drawing two marbles one after another without replacement.

Total number of outcomes =3×2=6

Then, the sample space is given by ={(R,G),(R,B),(G,R),(G,B),(B,R),(B,G)}

Want to see more full solutions like this?

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Answer 5

Textbook Question

100%

Answer 6

Textbook Question

100%

Answer 7

Expert Solution & Answer

To determine

To find: The sample space of given experiment with replacement and without

replacement.

Answer to Problem 2.1P

The sample space with replacement

={(R,R),(R,G),(R,B),(G,G),(G,R),(G,B),(B.,B),(B,R),(B,G)}

The sample space without replacement ={(R,G),(R,B),(G,R),(G,B),(B,R),(B,G)}

Explanation of Solution

Given information:

Consider box contains three marbles. They are 1 Red marble (R) , 1 Green marble (G) , 1

Blue marble (B) .

Calculation:

Sample space is the set of all possible outcomes of a random experiment.

Consider the experiment of drawing two marbles one after another with replacement.

Total number of outcomes =32

Then, the sample space is given by

={(R,R),(R,G),(R,B),(G,G),(G,R),(G,B),(B.,B),(B,R),(B,G)}

Consider the experiment of drawing two marbles one after another without replacement.

Total number of outcomes =3×2=6

Then, the sample space is given by ={(R,G),(R,B),(G,R),(G,B),(B,R),(B,G)}

Answer 8

Expert Solution & Answer

To determine

To find: The sample space of given experiment with replacement and without

replacement.

Answer to Problem 2.1P

The sample space with replacement

={(R,R),(R,G),(R,B),(G,G),(G,R),(G,B),(B.,B),(B,R),(B,G)}

The sample space without replacement ={(R,G),(R,B),(G,R),(G,B),(B,R),(B,G)}

Explanation of Solution

Given information:

Consider box contains three marbles. They are 1 Red marble (R) , 1 Green marble (G) , 1

Blue marble (B) .

Calculation:

Sample space is the set of all possible outcomes of a random experiment.

Consider the experiment of drawing two marbles one after another with replacement.

Total number of outcomes =32

Then, the sample space is given by

={(R,R),(R,G),(R,B),(G,G),(G,R),(G,B),(B.,B),(B,R),(B,G)}

Consider the experiment of drawing two marbles one after another without replacement.

Total number of outcomes =3×2=6

Then, the sample space is given by ={(R,G),(R,B),(G,R),(G,B),(B,R),(B,G)}

Answer 9

Expert Solution & Answer

Answer 10

Expert Solution & Answer

Answer 11

To determine

To find: The sample space of given experiment with replacement and without

replacement.

Answer 12

Answer to Problem 2.1P

The sample space with replacement

={(R,R),(R,G),(R,B),(G,G),(G,R),(G,B),(B.,B),(B,R),(B,G)}

The sample space without replacement ={(R,G),(R,B),(G,R),(G,B),(B,R),(B,G)}

Answer 13

Explanation of Solution

Given information:

Consider box contains three marbles. They are 1 Red marble (R) , 1 Green marble (G) , 1

Blue marble (B) .

Calculation:

Sample space is the set of all possible outcomes of a random experiment.

Consider the experiment of drawing two marbles one after another with replacement.

Total number of outcomes =32

Then, the sample space is given by

={(R,R),(R,G),(R,B),(G,G),(G,R),(G,B),(B.,B),(B,R),(B,G)}

Consider the experiment of drawing two marbles one after another without replacement.

Total number of outcomes =3×2=6

Then, the sample space is given by ={(R,G),(R,B),(G,R),(G,B),(B,R),(B,G)}

Answer 14

Ch. 2 - A box contains 3 marbles: 1 red, 1 green, and 1...Ch. 2 - In an experiment, die is rolled continually until...Ch. 2 - Two dice are thrown. Let E be the event that the...Ch. 2 - A, B, and C take turns flipping a coin. The first...Ch. 2 - A system is composed of 5 components, each of...Ch. 2 - A hospital administrator codes incoming patients...Ch. 2 - Consider an experiment that consists of...Ch. 2 - Suppose that A and B are mutually exclusive events...Ch. 2 - A retail establishment accepts either the American...Ch. 2 - Sixty percent of the students at a certain school...

A box contains 3 marbles: 1 red, 1 green, and 1 blue. Consider an experiment that consists of taking 1 marble from the box and then replacing it in the box and drawing a second marble from the box. Describe the sample space . Repeat when the second marble is drawn without replacing the first marble.

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