A2 June 2024 Q1

EdexcelCurrent spec6 marksDRVs

1. The discrete random variable \(X\) has the following probability distribution

\(x\)	\(-1\)	0	1	3	5
\(\mathrm{P}(X = x)\)	0.2	0.1	0.2	0.25	0.25

(a) Find \(\mathrm{Var}(X)\) (3)

(b) Find \(\mathrm{Var}(X^2)\) (3)

Mark scheme (a)

Scheme	Marks	AO
\(\mathrm{E}(X) = [-1 \times 0.2 + 0 + 1 \times 0.2] + 3 \times 0.25 + 5 \times 0.25\ [= 2]\)	M1	1.1b
\(\mathrm{E}(X^2) = (-1)^2 \times 0.2 + 0 + 1 \times 0.2 + 3^2 \times 0.25 + 5^2 \times 0.25\ [= 8.9]\)	M1	1.1b
[\(\mathrm{Var}(X) = 8.9 - 4 =\)] 4.9	A1	1.1b
	(3)

1^st M1 for an attempt at \(\mathrm{E}(X)\), at least the final 2 products seen or an answer of 2

2^nd M1 for attempting a correct expression for \(\mathrm{E}(X^2)\), at least 3 non-zero products seen

A1 for 4.9 or exact equivalent

Mark scheme (b)

Scheme	Marks	AO
\(\mathrm{E}(X^4) = (-1)^4 \times 0.2 + 0 + 1 \times 0.2 + 3^4 \times 0.25 + 5^4 \times 0.25\ [= 176.9]\)	M1	2.1
\(\mathrm{Var}(X^2) = \text{“}176.9\text{”} - \text{“}8.9\text{”}^2\)	M1	1.1b
\(= 97.69\) awrt 97.7	A1	1.1b
	(3)
	(6 marks)

1^st M1 for attempting a correct expression, at least 3 non-zero products seen (implied by 176.9)

2^nd M1 for a correct method, ft their 176.9 and their 8.9 but must be intending \(\mathrm{E}(X^4)\) and \(\mathrm{E}(X^2)\)

A1 for 97.69 or awrt 97.7