Lesson 5.02f-i
5.02f-i Geometric and Poisson distributions Quiz: OCR Further Maths, Unit 2
20 questions
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Lesson 5.02f-i, Geometric and Poisson distributions: 20 multiple choice questions for the OCR Further Maths (H245), Unit 2: Statistics (Y542), written with Revision Ninja.
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The 20 questions
-
What parameter defines a Geometric distribution X ~ Geo(p)?
- Sample variance
- Number of trials
- Mean rate
- Probability of success
-
What is the formula for P(X = r) for X ~ Geo(p), where q = 1 - p?
- q^r p
- q^(r-1) p
- (1-p)^r
- p^r q
-
What is the expected value E(X) of a random variable X ~ Geo(p)?
- 1 - p
- 1 / p
- (1-p) / p
- p
-
What is the variance Var(X) of a random variable X ~ Geo(p), where q = 1 - p?
- 1 / p^2
- q / p
- q / p^2
- p / q^2
-
What is the simplified expression for P(X > r) when X ~ Geo(p) and q = 1 - p?
- q^(r-1)
- 1 - q^r
- p^r
- q^r
-
Which parameter defines a Poisson distribution X ~ Po(lambda)?
- Number of trials
- Mean rate
- Probability of success
- Sample variance
-
For a Poisson distribution X ~ Po(lambda), how do the mean and variance compare?
- They are equal
- Sum equals one
- Variance is larger
- Mean is larger
-
What is the probability mass function formula for P(X = 0) in X ~ Po(lambda)?
- e^lambda
- 1 - e^(-lambda)
- lambda e^(-lambda)
- e^(-lambda)
-
If X ~ Geo(0.2), what is the expected value E(X)?
- 2
- 0.2
- 0.8
- 5
-
If X ~ Geo(0.1), what is the probability P(X > 2)?
- 0.81
- 0.01
- 0.19
- 0.09
-
If X ~ Geo(0.5), what is the exact value of P(X = 3)?
- 0.125
- 0.375
- 0.25
- 0.5
-
If X ~ Po(2) and Y ~ Po(3) are independent, what distribution does X + Y follow?
- Po(2.5)
- Po(5)
- Po(1)
- Po(6)
-
Calls arrive at 4 per hour. What is the mean number of calls in 30 minutes?
- 12
- 8
- 4
- 2
-
A Poisson random variable has a variance of 9. What is its mean?
- 4.5
- 81
- 3
- 9
-
What is the mode of any Geometric distribution X ~ Geo(p)?
- 0
- 1
- p
- 1/p
-
If X ~ Po(3), what is the formula expression for P(X = 1)?
- 3 e^(-3)
- e^(-3)
- 9 e^(-3)
- 1.5 e^(-3)
-
Which property states that P(X > s + t | X > s) = P(X > t)?
- Symmetry property
- Additive property
- Memoryless property
- Scaling property
-
Under what conditions does Bin(n, p) approximate to a Poisson distribution Po(lambda)?
- Small n, small p
- Small n, large p
- Large n, small p
- Large n, p = 0.5
-
Which assumption is essential for modelling events with a Poisson distribution?
- Probabilities change
- Events occur independently
- Fixed trial number
- Two outcomes only
-
For X ~ Geo(0.4), what is the value of P(X <= 2)?
- 0.36
- 0.64
- 0.84
- 0.16
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