Lesson Example Discussion Quiz: Class Homework |
Step-2 |
Title: Mean and variance of discrete random variable |
Grade: 9-a Lesson: S4-L2 |
Explanation: Hello Students, time to practice and review the steps for the problem. |
| Step | Type | Explanation | Answer |
|---|---|---|---|
1 |
Problem |
The probabilities that a batch of 4 computers will contain 0, 1, 2, 3 and 4 defective computers are 0.45, 0.39, 0.13, 0.01 and 0.0010, respectively. What is the standard deviation for the probability distribution.? |
|
2 |
Formula: |
Mean E(X) = \$\sum_{i=1}^n x_i p_i(x)\$ |
|
3 |
Step |
Finding the mean |
E(X) = (0×0.45) + (1×0.39) + (2×0.13) + (3×0.01) + (4×0.0010) |
4 |
Step |
Mean |
E(X) = 0.684 |
5 |
Formula: |
Variance \$VAR(X) = E(X^2) - (E(X))^2\$ |
|
6 |
Step |
Calculating \$E(X^2)\$ |
\$((0^2)×0.45) + ((1^2)×0.39) + ((2^2)×0.13) + ((3^2)×0.01) + ((4^2)×0.0010)\$ |
7 |
Step |
After simplification |
\$E(X^2)\$ = 1.016 |
8 |
Step |
Substitute \$E(X^2)\$ = 1.016,E(X) = 0.684 in VAR(X) |
|
9 |
Step |
VAR(X) |
\$1.016 - 0.684^2\$ |
10 |
Step |
Simplification |
\$1.016 - 0.4678\$ |
11 |
Step |
After simplification |
VAR(X) = 0.55 |
12 |
Step |
Mean and variance |
E(X) = 0.684,VAR(X) = 0.55 |
13 |
Answer |
D |
|
Tutor: Questions
| Seq | Type | Question | Audio |
|---|---|---|---|
1 |
Problem |
What did you learn from this problem? |
|
2 |
Clue |
What did you learn from the clues? |
|
3 |
Hint |
What did you learn from the Hints? |
|
4 |
Step |
What did you learn from the Steps? |
|
5 |
Step |
How can we improve the Steps? |
Copyright © 2020-2022 saibook.us Contact: info@saibook.us Version: 1.5 Built: 27-February-2023 06:00 AM EST