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Practise

Question bank

Original exam-style questions, mapped to your syllabus. Answers are checked for mathematical equivalence and every attempt updates your mastery.

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12 questions

SA-9709-P6-CR2-0012 marksL1 FoundationCalculatorE(X)
f(x)=x8f(x)=\tfrac x8 for 0≤x≤40\le x\le4, and 00 otherwise. Find E(X)E(X).

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P6-CR2-0032 marksL1 FoundationCalculatorE(X)
f(x)=38x2f(x)=\tfrac38x^2 for 0≤x≤20\le x\le2, and 00 otherwise. Find E(X)E(X).

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P6-CR2-0051 markL1 FoundationCalculatorE(X)
f(x)=34x(2−x)f(x)=\tfrac34x(2-x) for 0≤x≤20\le x\le2, and 00 otherwise. Write down E(X)E(X).

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P6-CR-Q021 markL1 FoundationCalculatorE(X)
For a continuous random variable, E(X)E(X) is
Choose one option

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P6-CR-0024 marksL2 StandardCalculatorE(X)
For f(x)=x29f(x)=\tfrac{x^2}9 on 0≤x≤30\le x\le3, find E(X)E(X) and Var(X)\text{Var}(X).

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P6-CR-0093 marksL2 StandardCalculatorVar(X)
f(x)=x2f(x)=\tfrac x2 for 0≤x≤20\le x\le2, and 00 otherwise. Find Var(X)\text{Var}(X).

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P6-CR2-0023 marksL2 StandardCalculatorVar(X)
For f(x)=x8f(x)=\tfrac x8 on 0≤x≤40\le x\le4 (with E(X)=83E(X)=\tfrac83), find Var(X)\text{Var}(X).

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P6-CR2-0043 marksL2 StandardCalculatorVar(X)
For f(x)=38x2f(x)=\tfrac38x^2 on 0≤x≤20\le x\le2, with E(X)=1.5E(X)=1.5, find Var(X)\text{Var}(X).

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P6-CR2-0062 marksL2 StandardCalculatorVar(X)
A continuous random variable has E(X)=1.5E(X)=1.5 and Var(X)=0.15\text{Var}(X)=0.15. Find E(2X+3)E(2X+3) and Var(2X+3)\text{Var}(2X+3).

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P6-CR2-0083 marksL2 StandardCalculatorVar(X)
XX is uniformly distributed on [0,6][0,6], so f(x)=16f(x)=\tfrac16 for 0≤x≤60\le x\le6. Find Var(X)\text{Var}(X).

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P6-CR-0054 marksL3 ExamCalculatorE(X)
f(x)=3x4f(x)=\dfrac3{x^4} for x≥1x\ge1, and 00 otherwise. Find E(X)E(X) and P(X>2)P(X>2).

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P6-CR2-0073 marksL3 ExamCalculatorE(X)
f(x)=2x2f(x)=\dfrac2{x^2} for 1≤x≤21\le x\le2, and 00 otherwise. Find E(X)E(X), correct to 3 significant figures.

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Salam Academy Original Practice · Proposed mark scheme