Pearson Edexcel IAL Mathematics S1.5.3 Mean & variance of a discrete

Practise calculating E(X), E(X^2) and Var(X) from tables, then applying linear transformations to random variables.

[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 S1.5.3 - Mean and variance of a discrete question 1 — Edexcel A-Level Mathematics AS

(a)

Show that E(A)=3.5

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$[\mathrm{E}(A)=] 1 \times 0.4+4 \times 0.2+5 \times 0.25+7 \times 0.15$ $=\underline{3.5} \quad(*)$

(b)

Find $\operatorname{Var}(A)$

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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$\left[\mathrm{E}\left(A^{2}\right)=\right] 1 \times 0.4+4^{2} \times 0.2+5^{2} \times 0.25+7^{2} \times 0.15[=17.2]$ $\operatorname{Var}(A)=\mathrm{E}\left(A^{2}\right)-[\mathrm{E}(A)]^{2}=17.2-3.5^{2}$ $=\underline{4.95}$

(3)

(c)

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

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

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 $\mu$ and their value of B is taken as their value of $\sigma$ . The person with the larger value of P(X>3.5) is the winner.

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S1.5.3 - Mean and variance of a discrete question 1

Question (a)

Question (b)

Question (c)