Lesson Example Discussion Quiz: Class Homework |
Step-3 |
Title: Poisson distribution |
Grade: 9-a Lesson: S4-L5 |
Explanation: Hello Students, time to practice and review the steps for the problem. |
Lesson Steps
| Step | Type | Explanation | Answer |
|---|---|---|---|
1 |
Problem |
Find the probability. P ( µ – σ < X < µ + σ ) if X has a Poisson distribution with λ = 5 |
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2 |
Step |
Given. |
λ = 5 |
3 |
Formula: |
Mean and variance of poisson distribution. |
mean = variance = λ |
4 |
Step |
Mean. |
µ = λ = 5 |
5 |
Step |
Variance. |
\$σ^2\$ = λ = 5 |
6 |
Step |
Solving for 'σ'. |
σ = \$\sqrt 5\$ = 2.236 |
7 |
Step |
Substitute the values in probability. |
P ( µ – σ < X < µ + σ ) = P( 5 - 2.236 < X < 5 + 2.236) |
8 |
Step |
Solving the probability. |
P(2.764 < X < 7.236) = P(3≤X≤7) |
9 |
Step |
P(3≤X≤7). |
P(X=3) + P(X=4) + P(X=5) + P(X=6) + P(X=7) |
10 |
Formula: |
Poisson distribution P(X=x) = \$(e^(-λ) λ^x)/x!\$ |
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11 |
Step |
P(3≤X≤7). |
\$(e^(-5) 5^3)/(3!) + (e^(-5) 5^4)/(4!) + (e^(-5) 5^5)/(5!) + (e^(-5) 5^6)/(6!) + (e^(-5) 5^7)/(7!)\$ |
12 |
Step |
P(3≤X≤7). |
\$(2.718^(-5) 5^3)/(3!) + (2.718^(-5) 5^4)/(4!) + (2.718^(-5) 5^5)/(5!) + (2.718^(-5) 5^6)/(6!) + (2.718^(-5) 5^7)/(7!)\$ |
13 |
Step |
P(3≤X≤7). |
0.1404 + 0.1755 + 0.1755 + 0.1462 + 0.1044 |
14 |
Step |
P(3≤X≤7). |
0.742 |
15 |
Answer |
B |
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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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