Lesson SA4-SA5
SA4-SA5 Expectation and linear functions Quiz: AQA Further Maths, Unit 4
20 questions
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Lesson SA4-SA5, Expectation and linear functions: 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
-
Which formula calculates the expected value E(X) for a discrete random variable?
- Sum of P(X = x)
- Sum of x P(X = x)
- Sum of x^2 P(X = x)
- Sum of x / P(X = x)
-
Which formula calculates E(X^2) for a discrete random variable?
- Sum of x^2 P(X = x)
- Sum of x P(X = x)
- Sum of x^2 / P(X = x)
- (Sum of x P(X = x))^2
-
Which formula gives the variance of a discrete random variable X?
- Var(X) = [E(X)]^2 - E(X^2)
- Var(X) = E(X) - E(X)^2
- Var(X) = E(X^2) + [E(X)]^2
- Var(X) = E(X^2) - [E(X)]^2
-
For constants a and b, which expression gives E(aX + b)?
- a E(X) + b
- E(X) + a b
- a E(X) + b squared
- a + E(X) + b
-
For constants a and b, which expression gives Var(aX + b)?
- a^2 Var(X) + b^2
- a Var(X)
- a Var(X) + b
- a^2 Var(X)
-
Which formula calculates E(g(X)) for a discrete random variable X?
- g(Sum of x P(X = x))
- Sum of P(g(x))
- Sum of g(x) P(X = x)
- Sum of g(x)
-
What is the expectation of a constant c?
- c
- c divided by 2
- 0
- c squared
-
A discrete random variable X takes values 1, 2 and 3 with probabilities 0.2, 0.5 and 0.3. What is E(X)?
- 2
- 2.1
- 2.5
- 1.9
-
For the same variable X taking values 1, 2 and 3 with probabilities 0.2, 0.5 and 0.3, what is E(X^2)?
- 4.9
- 2.1
- 4.41
- 6.0
-
For the same variable X taking values 1, 2 and 3 with probabilities 0.2, 0.5 and 0.3, what is Var(X)?
- 4.41
- 4.9
- 0.7
- 0.49
-
For the same variable X, let Y = 3X + 2. What is E(Y)?
- 8.3
- 6.3
- 11.6
- 4.1
-
For the same variable X, let Y = 3X + 2. What is Var(Y)?
- 4.41
- 0.49
- 1.47
- 2.94
-
For the same variable X taking values 1, 2 and 3 with probabilities 0.2, 0.5 and 0.3, what is E(X^3)?
- 8.3
- 9.26
- 12.3
- 4.9
-
A random variable X has E(X) = 4 and Var(X) = 3. What is E(2X - 5)?
- 13
- -3
- 8
- 3
-
A random variable X has E(X) = 4 and Var(X) = 3. What is Var(2X - 5)?
- 24
- 6
- 3
- 12
-
A discrete random variable X has E(X) = 2 and E(X^2) = 10. What is Var(X)?
- 6
- 8
- 10
- 4
-
Two independent random variables X and Y have Var(X) = 2 and Var(Y) = 3. What is Var(X + Y)?
- 2.5
- 6
- 5
- 1
-
A discrete random variable has P(X = x) = x/6 for x = 1, 2, 3. What is E(X)?
- 3
- 7/3
- 2
- 14/3
-
A random variable X has E(X) = 3 and Var(X) = 4. Y = aX + b has E(Y) = 0 and Var(Y) = 16, with a > 0. What are a and b?
- a = 2, b = 6
- a = 4, b = -6
- a = 2, b = -6
- a = -2, b = 6
-
A discrete random variable X takes values -1, 0 and 1 with probabilities 0.25, 0.5 and 0.25. What is Var(X)?
- 0.25
- 0.5
- 1
- 0
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