Lesson SB3-SB4
SB3-SB4 Mean, variance and sums of Poisson distributions Quiz: AQA Further Maths, Unit 4
20 questions
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Lesson SB3-SB4, Mean, variance and sums of Poisson distributions: 20 multiple choice questions for the AQA Further Maths (7367), Unit 4: Optional application 2: statistics, written with Revision Ninja.
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The 20 questions
-
For a Poisson random variable X ~ Po(lambda), what is the expectation E(X)?
- sqrt(lambda)
- lambda^2
- lambda
- 1 / lambda
-
For X ~ Po(lambda), what is Var(X)?
- 1/lambda
- 2 lambda
- lambda
- lambda squared
-
For X ~ Po(lambda), what is the standard deviation of X?
- lambda squared
- sqrt(lambda)
- 1 / sqrt(lambda)
- lambda
-
If independent variables X ~ Po(3) and Y ~ Po(4) are added, what is X + Y?
- Po(7)
- Po(3.5)
- Po(12)
- Po(1)
-
Why is the difference X - Y of two independent Poisson variables NOT Poisson?
- Is continuous
- Can be negative
- Has zero mean
- Has infinite variance
-
Which sample relationship between mean and variance suggests a Poisson distribution?
- Mean equals variance
- Variance exceeds mean
- Mean exceeds variance
- Mean is double variance
-
If X ~ Po(lambda) and Y ~ Po(mu) are independent, what is Var(X + Y)?
- lambda mu
- (lambda + mu)^2
- lambda + mu
- sqrt(lambda + mu)
-
X ~ Po(3) and Y ~ Po(4) are independent. What is P(X + Y = 0) to 6 decimal places in terms of e?
- e^(-7), about 0.000912
- e^(-4), about 0.0183
- e^(-12), about 0.00000614
- e^(-3), about 0.0498
-
X ~ Po(2) and Y ~ Po(5) are independent. What is Var(X + Y)?
- 10
- 2.5
- sqrt(7)
- 7
-
X ~ Po(16). What is the standard deviation of X?
- 8
- 256
- 16
- 4
-
X ~ Po(3) and Y ~ Po(5) are independent. What is E(X + Y)?
- 15
- 2
- 8
- 3.5
-
X ~ Po(4) per hour and Y ~ Po(2) per hour are independent. What is P(X + Y = 0) for one hour, to 4 decimal places?
- 0.1353
- 0.0498
- 0.0183
- 0.0025
-
X ~ Po(3). What is Var(2X)?
- 12
- 3
- 6
- 9
-
X ~ Po(4) and Y ~ Po(6) are independent. What is the standard deviation of X + Y?
- 10
- sqrt(6), about 2.45
- sqrt(10), about 3.16
- 4
-
Over three hours the total number of events is Po(9). If each hour is Po(lambda) and the hours are independent, what is lambda?
- 1/3
- 3
- 27
- 9
-
For X ~ Po(lambda), what is E(X^2) in terms of lambda?
- lambda + lambda squared
- lambda squared
- 2 lambda
- lambda
-
For X ~ Po(3), what is E(X^2)?
- 12
- 9
- 3
- 6
-
X ~ Po(2) and Y ~ Po(3) are independent. What is P(X + Y = 1) in terms of e, to 4 decimal places?
- 5e^(-5), about 0.0337
- e^(-5)/5, about 0.0013
- 3e^(-3), about 0.1494
- 2e^(-2), about 0.2707
-
X ~ Po(4) and Y ~ Po(1) are independent. What is P(X + Y >= 2) to 4 decimal places?
- 0.0337
- 0.9500
- 0.9596
- 0.0404
-
X1, X2 and X3 are independent, each Po(2). What is P(X1 + X2 + X3 = 0)?
- e^(-6)
- 3e^(-2)
- e^(-8)
- e^(-2)
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