A-LevelMathematicsProbability and statistics9709/62 · May/June 2024 · Q46 Marks
A random variable X has the distribution N(10, 12). Two independent values of X, denoted by X₁ and X₂, are chosen at random.
- (a)Write down the value of P(X₁ > X₂).[1]
- (b)Find P(X₁ > 2X₂ −3).[5]
Mark scheme
Marking points from the official mark scheme (May/June 2024). The mark or mark type is shown in brackets.
- [B1] 0.5
- [B1] E(X₁ - 2X₂ + 3) = 10 - 20 + 3 [= -7] or E(2X₂ - X₁ - 3) = 20 - 10 - 3 [= 7] Or equivalent using X₁ – 2X₂ = 10 – 20 [= −10] or 2X₂ - X₁ = 20 – 10 [= +10].
- [B1] Var(X₁ - 2X₂ + 3) = 12 + 2² × 12 + 0 [= 60]
- [M1] 0-(-7) / √'60' [= 0.904] Or numerator 3- '10' or -3-('-10'), but not '-3 -10' (i.e. numerator must be '7' or '-7').
- [M1] 1 – Φ('0.904') For area consistent with their working.
- [A1] = 0.183
Write your answer and get it marked
On Oracle Prep you can write or photograph your own answer and have it marked by AI against this mark scheme, with feedback on what you missed.
Sign up free →