Lesson Example Discussion Quiz: Class Homework |
Step-1 |
Title: Continuous random variable |
Grade: 9-a Lesson: S4-L7 |
Explanation: Hello Students, time to practice and review the steps for the problem. |
Lesson Steps
| Step | Type | Explanation | Answer |
|---|---|---|---|
1 |
Problem |
Consider a andom variable X with probability density function \$f(x) = \begin{cases} 4x^3,for & 0≤x≤1 \\ 0,& otherwise \\ \end{cases}\$.Find mean and variance. |
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2 |
Formula: |
E(X) = \$\int_-\infty^\infty\$x f(x)dx |
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3 |
Step |
Substitute f(x) in the formula |
E(X) = \$\int_0^1 x 4x^3\$ dx |
4 |
Step |
Simplification |
E(X) = 4 \$(x^5/5)_0^1\$ |
5 |
Step |
After simplification |
\$E(X) = 4/5\$ |
6 |
Formula: |
\$E(X^2)[\int_-\infty^\infty x^2\$ f(x)dx |
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7 |
Step |
Substitute f(x) in the formula |
E(X) = \$\int_0^1 x^2 4x^3\$ dx |
8 |
Step |
Simplification |
\$E(X^2) =\int_0^1 4x^5\$ dx |
9 |
Step |
Simplification |
\$E(X^2) =4(x^6/6)_0^1\$ |
10 |
Step |
After simplification |
\$E(X^2) = 4/6\$ |
11 |
Formula: |
V(X) = \$E(X^2) - (E(X))^2\$ |
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12 |
Step |
Simplification |
V(X) = \$4/6 - (4/5)^2\$ |
13 |
Step |
After simplification |
V(X) = \$4/6 - 16/25\$ |
14 |
Step |
After simplification |
V(X) = \$2/75\$ |
15 |
Answer |
D |
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Tutor: Questions
| Seq | Type | Question | Audio |
|---|---|---|---|
1 |
Problem |
What did you learn from this problem? |
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2 |
Clue |
What did you learn from the clues? |
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3 |
Hint |
What did you learn from the Hints? |
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4 |
Step |
What did you learn from the Steps? |
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5 |
Step |
How can we improve the Steps? |
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