Lesson 3B.2.1
3B.2.1 The Poisson distribution Quiz: Pearson Edexcel Further Maths, Unit 11
20 questions
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Lesson 3B.2.1, The Poisson distribution: 20 multiple choice questions for the Pearson Edexcel Further Maths (9FM0), Unit 11: Poisson and binomial distributions, written with Revision Ninja.
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The 20 questions
-
What is the probability mass function P(X = x) for X ~ Po(λ)?
- e^(-λ) λ^x / x!
- e^(-λ) x^λ / x!
- λ^x e^(-x) / λ!
- e^(λ) λ^x / x!
-
For a random variable X ~ Po(λ), what are its mean and variance?
- Both equal λ
- λ and λ^2
- λ and √λ
- np and np(1-p)
-
If X ~ Po(lambda) and Y ~ Po(mu) are independent, what is the distribution of X + Y?
- Po(lambda mu)
- Po(lambda - mu)
- Po(lambda + mu + 1)
- Po(lambda + mu)
-
What three conditions are required to model a variable using a Poisson distribution?
- Random, independent, constant rate
- Fixed trials, independent, success
- Normal, continuous, constant mean
- Dependent, constant rate, bounded
-
If the number of events per minute is Po(lambda), what is the distribution of the number of events in 5 minutes?
- Po(5 lambda)
- Po(lambda)
- Po(lambda^5)
- Po(lambda / 5)
-
If X ~ Po(3), what is P(X = 0) to 4 decimal places?
- 0.9502
- 0.0498
- 20.0855
- 0.1494
-
If X ~ Po(2), what is P(X = 2) to 4 decimal places?
- 0.2707
- 0.6767
- 0.5413
- 0.1353
-
If X ~ Po(1.5), what is P(X <= 1) to 4 decimal places?
- 0.2231
- 0.5578
- 0.3347
- 0.7769
-
If X ~ Po(4), what is P(X >= 1) to 4 decimal places?
- 0.5000
- 0.9817
- 0.0183
- 0.0733
-
X ~ Po(2) and Y ~ Po(3) are independent. What is P(X + Y = 0) to 4 decimal places?
- 0.0337
- 0.0025
- 0.0067
- 0.3679
-
Calls to a help line follow Po(6) per hour. What is the expected number of calls in 15 minutes?
- 2.5
- 1.5
- 0.4
- 6
-
If X ~ Po(lambda) and P(X = 1) = P(X = 2), what is lambda?
- 3
- 4
- 1
- 2
-
If X ~ Po(2), what is P(X = 3 | X >= 1) to 3 decimal places?
- 0.209
- 0.135
- 0.271
- 0.181
-
If X ~ Po(lambda) and P(X = 0) = 0.2, what is lambda?
- ln 5, about 1.609
- 5
- 0.2
- ln 0.2, about -1.609
-
A call centre receives 4 calls per 10 minutes on average, modelled as Poisson. What is the probability of no calls in 5 minutes, to 3 decimal places?
- 0.018
- 0.368
- 0.135
- 0.271
-
X1, X2 and X3 are independent, each Po(2). What is P(X1 + X2 + X3 = 6) to 4 decimal places?
- 0.0900
- 0.0025
- 0.1606
- 0.4463
-
Which condition must hold for the sum of two Poisson variables to also be Poisson?
- Identical variance
- Equal mean values
- They are independent
- Continuous rates
-
Which scenario is best modelled using a Poisson distribution?
- Coin tosses until heads
- Exam scores out of 100
- Emails arriving per hour
- Heights of adult humans
-
If X ~ Po(2), what is E(X^2)?
- 2
- 8
- 6
- 4
-
If X ~ Po(3), what is P(X = 0) + P(X = 1) to 4 decimal places?
- 0.1991
- 0.4232
- 0.0498
- 0.1494
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