### Probability Distribution and Expected ValueConsider the following probability distribution:| \( x_i \) | P(X = \( x_i \)) ||------|---------------|| 0 | 0.1 || 1 | 0.2 || 2 | 0.3 || 3 | 0.4 |To determine the expected value, we use the formula for the expected value of a discrete random variable:\[ E(X) = \sum (x_i \cdot P(X = x_i)) \]Where \( x_i \) are the possible values of the random variable \( X \), and \( P(X = x_i) \) are the corresponding probabilities.**Question:** The expected value is ______.#### Multiple Choice:- 2.5- 0.9#### Answer:To calculate the expected value, we multiply each \( x_i \) value by its corresponding probability and sum the results:\[ E(X) = (0 \cdot 0.1) + (1 \cdot 0.2) + (2 \cdot 0.3) + (3 \cdot 0.4) \]\[ E(X) = 0 + 0.2 + 0.6 + 1.2 \]\[ E(X) = 2.0 \]So, the expected value is 2.0. However, since the given options are 2.5 and 0.9, the accurate expected value is not provided in the given choices. The provided options might contain an error.

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Answered: Consider the following probability…

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Consider the following probability distribution. Xi 0 1 2 3 P(X = X i) 0.1 0.2 0.3 0.4 The expected value is

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.8: Probability

Problem 47E

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Question

### Probability Distribution and Expected Value

Consider the following probability distribution:

| \( x_i \) | P(X = \( x_i \)) |
|------|---------------|
| 0 | 0.1 |
| 1 | 0.2 |
| 2 | 0.3 |
| 3 | 0.4 |

To determine the expected value, we use the formula for the expected value of a discrete random variable:

\[ E(X) = \sum (x_i \cdot P(X = x_i)) \]

Where \( x_i \) are the possible values of the random variable \( X \), and \( P(X = x_i) \) are the corresponding probabilities.

**Question:** The expected value is ______.

#### Multiple Choice:

- 2.5
- 0.9

#### Answer:
To calculate the expected value, we multiply each \( x_i \) value by its corresponding probability and sum the results:

\[ E(X) = (0 \cdot 0.1) + (1 \cdot 0.2) + (2 \cdot 0.3) + (3 \cdot 0.4) \]
\[ E(X) = 0 + 0.2 + 0.6 + 1.2 \]
\[ E(X) = 2.0 \]

So, the expected value is 2.0. However, since the given options are 2.5 and 0.9, the accurate expected value is not provided in the given choices. The provided options might contain an error.

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