3:14 PM Sat Nov 20 * O C 57% AA www-awu.aleks.com Home | iCar Bb Upload Assi... Week 6 - AL... A Use your tex... b My Question... tatistic... 5... Week 6 - ALEKS Quiz 3 Time Remaining: 1:55:03 ● Opeyemi Question 2 of 5 (6 points) Question Attempt: 1 of 1 Español 1 2 3 4 Let X be a random variable with the following probability distribution. Value x of X P(X=x) 10 0.15 20 0.15 30 0.15 40 0.20 50 0.25 60 0.10 Complete the following. (If necessary, consult a list of formulas.) (a) Find the expectation E (X) of X. E (x) = D (b) Find the variance Var(X) of X. Var (x) = D
3:14 PM Sat Nov 20 * O C 57% AA www-awu.aleks.com Home | iCar Bb Upload Assi... Week 6 - AL... A Use your tex... b My Question... tatistic... 5... Week 6 - ALEKS Quiz 3 Time Remaining: 1:55:03 ● Opeyemi Question 2 of 5 (6 points) Question Attempt: 1 of 1 Español 1 2 3 4 Let X be a random variable with the following probability distribution. Value x of X P(X=x) 10 0.15 20 0.15 30 0.15 40 0.20 50 0.25 60 0.10 Complete the following. (If necessary, consult a list of formulas.) (a) Find the expectation E (X) of X. E (x) = D (b) Find the variance Var(X) of X. Var (x) = D
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
Related questions
Question
![### Probability Distribution and Calculation of Expectation and Variance
#### Probability Distribution Table
The random variable \( X \) has the following probability distribution:
| Value \( x \) of \( X \) | Probability \( P(X = x) \) |
|--------------------------|----------------------------|
| 10 | 0.15 |
| 20 | 0.15 |
| 30 | 0.15 |
| 40 | 0.20 |
| 50 | 0.25 |
| 60 | 0.10 |
#### Tasks
1. **Expectation of \( X \):**
- Find the expectation \( E(X) \).
2. **Variance of \( X \):**
- Find the variance \( \text{Var}(X) \).
To complete these calculations, you can use formulas for expected value and variance.
#### Calculation Steps
1. **Expectation \( E(X) \):**
\[
E(X) = \sum [x \times P(X = x)]
\]
2. **Variance \( \text{Var}(X) \):**
\[
\text{Var}(X) = \sum [(x - E(X))^2 \times P(X = x)]
\]
These computations will help in understanding the characteristics of the probability distribution.
Please refer to a comprehensive list of formulas if needed for further calculations.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F09eed710-0258-4407-814d-4e70d213c190%2F62914601-bd8c-4d17-a575-501215975073%2Fq3gv523_processed.png&w=3840&q=75)
Transcribed Image Text:### Probability Distribution and Calculation of Expectation and Variance
#### Probability Distribution Table
The random variable \( X \) has the following probability distribution:
| Value \( x \) of \( X \) | Probability \( P(X = x) \) |
|--------------------------|----------------------------|
| 10 | 0.15 |
| 20 | 0.15 |
| 30 | 0.15 |
| 40 | 0.20 |
| 50 | 0.25 |
| 60 | 0.10 |
#### Tasks
1. **Expectation of \( X \):**
- Find the expectation \( E(X) \).
2. **Variance of \( X \):**
- Find the variance \( \text{Var}(X) \).
To complete these calculations, you can use formulas for expected value and variance.
#### Calculation Steps
1. **Expectation \( E(X) \):**
\[
E(X) = \sum [x \times P(X = x)]
\]
2. **Variance \( \text{Var}(X) \):**
\[
\text{Var}(X) = \sum [(x - E(X))^2 \times P(X = x)]
\]
These computations will help in understanding the characteristics of the probability distribution.
Please refer to a comprehensive list of formulas if needed for further calculations.
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