Lesson Example Discussion Quiz: Class Homework |
Step-4 |
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) = (5×0.10) + (6×0.30) + (7×0.45) + (8×0.15) |
4 |
Step |
Mean |
E(X) = 6.65 |
5 |
Formula: |
Variance \$VAR(X) = E(X^2) - (E(X))^2\$ |
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6 |
Step |
Calculating \$E(X^2)\$ |
\$((5^2)×0.10) + ((6^2)×0.30) + ((7^2)×0.45) + ((8^2)×0.15)\$ |
7 |
Step |
After simplification |
\$E(X^2)\$ = 44.95 |
8 |
Step |
Substitute \$E(X^2)\$ = 44.95,E(X) = 6.65 in VAR(X) |
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9 |
Step |
VAR(X) |
\$44.95 - 6.65^2\$ |
10 |
Step |
Simplification |
\$44.95 - 44.225\$ |
11 |
Step |
After simplification |
VAR(X) = 0.72 |
12 |
Step |
Mean and variance |
E(X) = 6.65,VAR(X) = 0.72 |
13 |
Answer |
C |
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Tutor: Questions
| Seq | Type | Question | Audio |
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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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