Lesson Example Discussion Quiz: Class Homework |
Step-4 |
Title: Uniform distribution |
Grade: 9-a Lesson: S4-L8 |
Explanation: Hello Students, time to practice and review the steps for the problem. |
| Step | Type | Explanation | Answer |
|---|---|---|---|
1 |
Problem |
If X is a Uniform variable U(a,b) with first and third quartiles 100 and 200, find the p.d.f of X. |
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2 |
Step |
First quartiles |
\$Q_1 = 100\$ \$(3a+b)/4\$ = 100 \$3a+b = 400\$ \$b=400-3a\$⇒equation(1) |
3 |
Step |
First quartiles |
\$Q_3 = 200\$ \$(a+3b)/4\$ = 200 \$a+3b = 800\$ ⇒equation(2) |
4 |
Step |
Substitute equation(1) in (2) |
a+3(400-3a) = 800 a + 1200 - 9a = 800 -8a+1200 = 800 -8a = 800 -1200 -8a = -400 a=50 |
5 |
Step |
Substitute a=50 in equation(1) |
b=400-3(50) b = 400 - 150 b=250 |
6 |
Formula: |
Uniform distribution For X∼ U(a,b) f(x) = \$1/(b-a)\$ a<x<b |
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7 |
Step |
Substitute a=50,b=250 in formula |
f(x) = \$1/(250-50)\$ 50<x<250 |
8 |
Step |
Uniform distribution |
f(x) = \$1/200\$ 50<x<250 |
9 |
Answer |
A |
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Tutor: Questions
| Seq | Type | Question | Audio |
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1 |
Problem |
What did you learn from this 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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