Calculate Var(aX+b) transformations

Questions that ask specifically for the variance of a linear transformation Var(aX+b) after finding or using Var(X), requiring the variance transformation formula.

5 questions · Moderate -0.5

5.02c Linear coding: effects on mean and variance
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Edexcel S1 2017 January Q4
13 marks Moderate -0.3
  1. In a game, the number of points scored by a player in the first round is given by the random variable \(X\) with probability distribution
\(x\)5678
\(\mathrm { P } ( X = x )\)0.130.210.290.37
Find
  1. \(\mathrm { E } ( X )\)
  2. \(\operatorname { Var } ( X )\)
  3. \(\operatorname { Var } ( 3 - 2 X )\) The number of points scored by a player in the second round is given by the random variable \(Y\) and is independent of the number of points scored in the first round. The random variable \(Y\) has probability function $$\mathrm { P } ( Y = y ) = \frac { 1 } { 4 } \quad \text { for } y = 5,6,7,8$$
  4. Write down the value of \(\mathrm { E } ( Y )\)
  5. Find \(\mathrm { P } ( X = Y )\)
  6. Find the probability that the number of points scored by a player in the first round is greater than the number of points scored by the player in the second round.
AQA Further AS Paper 2 Statistics 2021 June Q1
1 marks Easy -1.2
1 The discrete random variable \(X\) has \(\operatorname { Var } ( X ) = 6.5\) Find \(\operatorname { Var } ( 4 X - 2 )\) Circle your answer.
2426102104
OCR Further Statistics AS 2018 June Q2
8 marks Moderate -0.5
2 The probability distribution for the discrete random variable \(W\) is given in the table.
\(w\)1234
\(\mathrm { P } ( W = w )\)0.250.36\(x\)\(x ^ { 2 }\)
  1. Show that \(\operatorname { Var } ( W ) = 0.8571\).
  2. Find \(\operatorname { Var } ( 3 W + 6 )\).
OCR Further Statistics 2021 November Q2
7 marks Moderate -0.3
2 A discrete random variable \(D\) has the following probability distribution, where \(a\) is a constant.
\(d\)0246
\(\mathrm { P } ( D = d )\)\(a\)0.10.30.2
Determine the value of \(\operatorname { Var } ( 3 D + 4 )\).
AQA Further AS Paper 2 Statistics 2020 June Q5
7 marks Moderate -0.3
The discrete random variable \(X\) has the following probability distribution.
\(x\)2469
P\((X = x)\)0.20.60.10.1
  1. Find P\((X \leq 6)\) [1 mark]
  2. Let \(Y = 3X + 2\) Show that Var\((Y) = 32.49\) [5 marks]
  3. The continuous random variable \(T\) is independent of \(Y\). Given that Var\((T) = 5\), find Var\((T + Y)\) [1 mark]