Edexcel A-level Further Maths coverage

Discrete probability distributions

Section FS1-1
1 spec leaf

Notes and three levels of exam-style practice for each registered specification leaf in this section.

Open the printable pack
FS1-1.1

Calculation of the mean and variance of discrete probability distributions. Extension of expected value function to include E(g(X)).

  • For a discrete random variable, E(X)=∑xP(X=x)E(X)=\sum xP(X=x) and Var⁡(X)=E(X2)−[E(X)]2\operatorname{Var}(X)=E(X^2)-[E(X)]^2.
  • For a function of the variable, calculate E[g(X)]=∑g(x)P(X=x)E[g(X)]=\sum g(x)P(X=x) over every possible value of XX.
  • For example, once E(X)E(X) and E(X2)E(X^2) are known, E[(X−a)2]=E(X2)−2aE(X)+a2E[(X-a)^2]=E(X^2)-2aE(X)+a^2 can be evaluated without rebuilding a table.
  • A common error is to write E[g(X)]=g(E(X))E[g(X)]=g(E(X)); this is not true in general.

Tier 1 · Easy

4 marks
ORIGINAL

The random variable XX takes values 0,1,2,40,1,2,4 with probabilities 0.15,0.25,0.35,0.250.15,0.25,0.35,0.25 respectively. Find E(X)E(X) and Var⁡(X)\operatorname{Var}(X).

Tier 2 · Standard

3 marks
ORIGINAL

The random variable XX takes values −2,1,3-2,1,3 with probabilities 0.2,0.5,0.30.2,0.5,0.3 respectively. Calculate E[(X+2)2]E[(X+2)^2].

Tier 3 · Hard

7 marks
ORIGINAL

The random variable XX takes values 0,1,3,50,1,3,5 with probabilities k,2k,3k,4kk,2k,3k,4k respectively. Find kk, E(X)E(X), Var⁡(X)\operatorname{Var}(X) and E[(X−2)2]E[(X-2)^2].