Apply E(aX+b) or Var(aX+b) formulas directly

Questions that give E(X) and/or Var(X) directly and ask to apply the standard formulas E(aX+b)=aE(X)+b or Var(aX+b)=a²Var(X) without needing to calculate from a distribution.

4 questions · Moderate -0.6

Sort by: Default | Easiest first | Hardest first

WJEC Further Unit 2 2019 June Q2

9 marks Challenging +1.2

2. The probability of winning a certain game at a funfair is \(p\). Aman plays the game 5 times and Boaz plays the game 8 times. The independent random variables \(X\) and \(Y\) denote the number of wins for Aman and Boaz respectively.

Given that \(\mathrm { E } ( X Y ) = 6 \cdot 4\), calculate \(p\).
Find \(\operatorname { Var } ( X Y )\).

AQA Further AS Paper 2 Statistics 2023 June Q1

1 marks Easy -1.2

1 The continuous random variable \(X\) has variance 9 The discrete random variable \(Y\) has standard deviation 2 and is independent of \(X\) Find \(\operatorname { Var } ( X + Y )\) Circle your answer.
5111385

AQA Further AS Paper 2 Statistics 2023 June Q3

3 marks Easy -1.2

3 The discrete random variable \(X\) has probability distribution

\(x\)	- 4	3	8
\(\mathrm { P } ( X = x )\)	0.2	0.7	0.1

Show that \(\mathrm { E } ( 5 X - 7 ) = 3.5\)

AQA Further Paper 3 Statistics 2019 June Q1

1 marks Easy -1.2

1 The discrete random variable \(X\) has \(\operatorname { Var } ( X ) = 5\) Find \(\operatorname { Var } ( 4 X - 3 )\) Circle your answer.
17207780