Define (a) random process, (b) random variable, (c) discrete random variable, and (d) probability distribution.

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Answer 1

Textbook Question

Chapter 6, Problem 1CR

Define (a) random process, (b) random variable, (c) discrete random variable, and (d) probability distribution.

(a)

Expert Solution

To determine

Define the term “random process”.

Explanation of Solution

Random process:

The random process is defined as the probability model which is assigned to the corresponding outcomes that exist in the sample space.

(b)

Expert Solution

To determine

Define the term “random variable”.

Explanation of Solution

Random variable:

The random variable is defined as the rule or function that assigns numerical values to all outcomes which exist in the sample space of a random experiment.

(c)

Expert Solution

To determine

Define the term “discrete random variable”.

Explanation of Solution

Discrete random variable:

The discrete random variable is a random variable which has the countable number of distinct values.

(d)

Expert Solution

To determine

Define the term “Probability distribution”.

Explanation of Solution

Probability Distribution:

The probability distribution assigns probabilities corresponding to the values of random variable.

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Answer 2

Textbook Question

Chapter 6, Problem 1CR

Define (a) random process, (b) random variable, (c) discrete random variable, and (d) probability distribution.

(a)

Expert Solution

To determine

Define the term “random process”.

Explanation of Solution

Random process:

The random process is defined as the probability model which is assigned to the corresponding outcomes that exist in the sample space.

(b)

Expert Solution

To determine

Define the term “random variable”.

Explanation of Solution

Random variable:

The random variable is defined as the rule or function that assigns numerical values to all outcomes which exist in the sample space of a random experiment.

(c)

Expert Solution

To determine

Define the term “discrete random variable”.

Explanation of Solution

Discrete random variable:

The discrete random variable is a random variable which has the countable number of distinct values.

(d)

Expert Solution

To determine

Define the term “Probability distribution”.

Explanation of Solution

Probability Distribution:

The probability distribution assigns probabilities corresponding to the values of random variable.

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Answer 3

Textbook Question

Chapter 6, Problem 1CR

Define (a) random process, (b) random variable, (c) discrete random variable, and (d) probability distribution.

(a)

Expert Solution

To determine

Define the term “random process”.

Explanation of Solution

Random process:

The random process is defined as the probability model which is assigned to the corresponding outcomes that exist in the sample space.

(b)

Expert Solution

To determine

Define the term “random variable”.

Explanation of Solution

Random variable:

The random variable is defined as the rule or function that assigns numerical values to all outcomes which exist in the sample space of a random experiment.

(c)

Expert Solution

To determine

Define the term “discrete random variable”.

Explanation of Solution

Discrete random variable:

The discrete random variable is a random variable which has the countable number of distinct values.

(d)

Expert Solution

To determine

Define the term “Probability distribution”.

Explanation of Solution

Probability Distribution:

The probability distribution assigns probabilities corresponding to the values of random variable.

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Answer 4

Textbook Question

Chapter 6, Problem 1CR

Define (a) random process, (b) random variable, (c) discrete random variable, and (d) probability distribution.

(a)

Expert Solution

To determine

Define the term “random process”.

Explanation of Solution

Random process:

The random process is defined as the probability model which is assigned to the corresponding outcomes that exist in the sample space.

(b)

Expert Solution

To determine

Define the term “random variable”.

Explanation of Solution

Random variable:

The random variable is defined as the rule or function that assigns numerical values to all outcomes which exist in the sample space of a random experiment.

(c)

Expert Solution

To determine

Define the term “discrete random variable”.

Explanation of Solution

Discrete random variable:

The discrete random variable is a random variable which has the countable number of distinct values.

(d)

Expert Solution

To determine

Define the term “Probability distribution”.

Explanation of Solution

Probability Distribution:

The probability distribution assigns probabilities corresponding to the values of random variable.

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Answer 5

Textbook Question

Answer 6

Textbook Question

Answer 7

(a)

Expert Solution

To determine

Define the term “random process”.

Explanation of Solution

Random process:

The random process is defined as the probability model which is assigned to the corresponding outcomes that exist in the sample space.

(b)

Expert Solution

To determine

Define the term “random variable”.

Explanation of Solution

Random variable:

The random variable is defined as the rule or function that assigns numerical values to all outcomes which exist in the sample space of a random experiment.

(c)

Expert Solution

To determine

Define the term “discrete random variable”.

Explanation of Solution

Discrete random variable:

The discrete random variable is a random variable which has the countable number of distinct values.

(d)

Expert Solution

To determine

Define the term “Probability distribution”.

Explanation of Solution

Probability Distribution:

The probability distribution assigns probabilities corresponding to the values of random variable.

Answer 8

(a)

Expert Solution

To determine

Define the term “random process”.

Explanation of Solution

Random process:

The random process is defined as the probability model which is assigned to the corresponding outcomes that exist in the sample space.

Answer 9

(a)

Expert Solution

Answer 10

(a)

Expert Solution

Answer 11

Expert Solution

Answer 12

To determine

Define the term “random process”.

Answer 13

Explanation of Solution

Random process:

The random process is defined as the probability model which is assigned to the corresponding outcomes that exist in the sample space.

Answer 14

(b)

Expert Solution

To determine

Define the term “random variable”.

Explanation of Solution

Random variable:

The random variable is defined as the rule or function that assigns numerical values to all outcomes which exist in the sample space of a random experiment.

Answer 15

(b)

Expert Solution

Answer 16

(b)

Expert Solution

Answer 17

Expert Solution

Answer 18

To determine

Define the term “random variable”.

Answer 19

Explanation of Solution

Random variable:

The random variable is defined as the rule or function that assigns numerical values to all outcomes which exist in the sample space of a random experiment.

Answer 20

(c)

Expert Solution

To determine

Define the term “discrete random variable”.

Explanation of Solution

Discrete random variable:

The discrete random variable is a random variable which has the countable number of distinct values.

Answer 21

(c)

Expert Solution

Answer 22

(c)

Expert Solution

Answer 23

Expert Solution

Answer 24

To determine

Define the term “discrete random variable”.

Answer 25

Explanation of Solution

Discrete random variable:

The discrete random variable is a random variable which has the countable number of distinct values.

Answer 26

(d)

Expert Solution

To determine

Define the term “Probability distribution”.

Explanation of Solution

Probability Distribution:

The probability distribution assigns probabilities corresponding to the values of random variable.

Answer 27

(d)

Expert Solution

Answer 28

(d)

Expert Solution

Answer 29

Expert Solution

Answer 30

To determine

Define the term “Probability distribution”.

Answer 31

Explanation of Solution

Probability Distribution:

The probability distribution assigns probabilities corresponding to the values of random variable.

Answer 32

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Define (a) random process, (b) random variable, (c) discrete random variable, and (d) probability distribution.

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