Lesson Example Discussion Quiz: Class Homework |
Step-1 |
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 |
Determine the mean and variance of the random variable X having the following probability distribution. |
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2 |
Formula: |
Mean E(X) = \$\sum_{i=1}^n x_i p_i(x)\$ |
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3 |
Step |
Finding the mean |
E(X) = (50×0.5) + (51×0.2) + (52×0.1) + (53×0.2) |
4 |
Step |
Mean |
E(X) = 51 |
5 |
Formula: |
Variance \$VAR(X) = E(X^2) - (E(X))^2\$ |
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6 |
Step |
Calculating \$E(X^2)\$ |
\$((50^2)×0.5) + ((51^2)×0.2) + ((52^2)×0.1) + ((53^2)×0.2)\$ |
7 |
Step |
After simplification |
\$E(X^2)\$ = 2602.4 |
8 |
Step |
Substitute \$E(X^2)\$ = 2602.4,E(X) = 51 in VAR(X) |
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9 |
Step |
VAR(X) |
\$2602.4 - 51^2\$ |
10 |
Step |
Simplification |
\$2602.4 - 2601\$ |
11 |
Step |
After simplification |
VAR(X) = 3.1 |
12 |
Step |
Mean and variance |
E(X) = 51, VAR(X) = 3.1 |
13 |
Answer |
B |
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Tutor: Questions
| Seq | Type | Question | Audio |
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1 |
Problem |
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2 |
Clue |
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3 |
Hint |
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4 |
Step |
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5 |
Step |
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