Lesson 3B.3.2-3B.3.3
3B.3.2-3B.3.3 Mean and variance of geometric and negative binomial distributions Quiz: Pearson Edexcel Further Maths, Unit 12
20 questions
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Lesson 3B.3.2-3B.3.3, Mean and variance of geometric and negative binomial distributions: 20 multiple choice questions for the Pearson Edexcel Further Maths (9FM0), Unit 12: Geometric and negative binomial distributions, written with Revision Ninja.
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The 20 questions
-
For a geometric distribution with parameter p, what is E(X)?
- 1/p^2
- (1 - p)/p
- 1/p
- p
-
For a geometric distribution with parameter p, what is Var(X)?
- p(1 - p)
- (1 - p)/p^2
- 1/p^2
- (1 - p)/p
-
For a negative binomial distribution with parameters r and p, what is E(X)?
- rp
- r/p
- r(1 - p)/p
- r/(1 - p)
-
For a negative binomial distribution with parameters r and p, what is Var(X)?
- rp^2/(1 - p)
- r(1 - p)/p^2
- r/p^2
- r(1 - p)/p
-
A geometric distribution has p = 0.2. What are its mean and variance?
- Mean 5, variance 20
- Mean 0.2, variance 5
- Mean 5, variance 5
- Mean 4, variance 16
-
A negative binomial distribution has r = 3 and p = 0.5. What is its mean?
- 3
- 12
- 6
- 1.5
-
A geometric distribution has p = 0.25. What is its variance?
- 3
- 4
- 12
- 1.5
-
A negative binomial distribution has r = 4 and p = 0.8. What is its variance?
- 4
- 0.8
- 1.25
- 5
-
How many rolls of a fair die are expected to be needed to get a six?
- 36
- 6
- 3.5
- 1/6
-
A geometric distribution has mean 4. What is p?
- 0.75
- 0.4
- 0.25
- 4
-
A geometric distribution has mean 5 and variance 20. What is p?
- 0.2
- 0.5
- 0.8
- 0.1
-
Each attempt succeeds with probability 0.1. What is the expected number of attempts needed to get 2 successes?
- 10
- 2
- 20
- 5
-
Each attempt succeeds with probability 0.1. What is the variance of the number of attempts needed to get 2 successes?
- 180
- 90
- 20
- 18
-
A geometric distribution has mean 8. What is P(X = 1)?
- 0.125
- 0.8
- 0.875
- 8
-
For a geometric distribution with mean m, which expression gives the variance in terms of m and p?
- m^2 (1 - p)
- m (1 - p)
- m^2 / p
- m (1 - p)/p
-
A negative binomial distribution has mean 12 and variance 24. What is r?
- 2
- 6
- 3
- 4
-
For a geometric distribution with p = 0.3, what is E(X^2)?
- 17/9
- 170/9
- 10/3
- 100/9
-
A negative binomial distribution has r = 2 and p = 0.25. What is its standard deviation to 2 decimal places?
- 2.45
- 8.00
- 4.90
- 24.00
-
A fair coin is tossed until two tails appear. What is the expected number of tosses?
- 4
- 2
- 3
- 1
-
Which negative binomial mean formula reduces to the geometric mean when r = 1?
- r/p gives 1/p
- r(1 - p)/p gives (1 - p)/p
- rp gives p
- r/(1 - p) gives 1/(1 - p)
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