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Edexcel A-Level Mathematics AS S1.5.3 Mean and Variance of a Discrete Questions

Practise calculating E(X), E(X²) and Var(X) from probability tables, applying linear transformations, and solving distribution constants from probability and mean conditions.

Syllabus
First assessment 2019
Course
Mathematics YMA01
Level
AS

Exam points

  • calculate E(X) and E(X^2) from a probability table before finding Var(X)
  • use E(aX+b) and Var(aX+b) to transform means or variances correctly
  • solve for constants in a distribution using total probability and conditions on E(X)

Edexcel A-Level Mathematics AS S1.5.3 Mean and Variance of a Discrete Questions question 1

[Maximum number: 6]

The random variable A represents the score when a spinner is spun. The probability distribution for A is given in the following table.

Table for Question Edexcel A-Level Mathematics AS S1.5.3 Mean and Variance of a Discrete Questions question 1 — Edexcel A-Level Mathematics AS

Question (a)

(a)

Show that E(A)=3.5

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Question (b)

(b)

Find Var⁡(A)\operatorname{Var}(A)

The random variable B represents the score on a 4 -sided die. The probability distribution for B is given in the following table where k is a positive integer.

Table for Question (b) — Edexcel A-Level Mathematics AS
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Question (c)

(c)

Given that E(B)=E(A) state, giving a reason, the value of k.

The random variable X∼ N(μ,σ2)X \sim \mathrm{~N}\left(\mu, \sigma^{2}\right)

Sam and Tim are playing a game with the spinner and the die.

They each spin the spinner once to obtain their value of A and each roll the die once to obtain their value of B.
Their value of A is taken as their value of μ\mu and their value of B is taken as their value of σ\sigma. The person with the larger value of P(X>3.5) is the winner.

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