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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-ST-PG-0011 markL1 FoundationNon-calculatorDefinition
For G(t)=14(1+2t+t2)G(t)=\frac14(1+2t+t^2), find P(X=1)P(X=1).

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Salam Academy Original Practice · Proposed mark scheme
SA-ST-PG-G012 marksL1 FoundationNon-calculatorDefinition
G(t)=k(1+2t+t2)G(t)=k(1+2t+t^2) is a PGF. Find kk.

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Salam Academy Original Practice · Proposed mark scheme
SA-ST-PG-Q011 markL1 FoundationNon-calculatorSums
For independent XX, YY, the PGF of X+YX+Y is
Choose one option

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Salam Academy Original Practice · Proposed mark scheme
SA-ST-PG-X011 markL1 FoundationNon-calculatorMoments
XX has PGF (0.7+0.3t)10(0.7+0.3t)^{10}. Find E(X)E(X).

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Salam Academy Original Practice · Proposed mark scheme
SA-ST-PG-X021 markL1 FoundationNon-calculatorDefinition
XX has PGF e3(t−1)e^{3(t-1)}. Find P(X=0)P(X=0) exactly.

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Salam Academy Original Practice · Proposed mark scheme
SA-ST-PG-0022 marksL2 StandardNon-calculatorMoments
For G(t)=14(1+2t+t2)G(t)=\frac14(1+2t+t^2), find E(X)E(X).

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Salam Academy Original Practice · Proposed mark scheme
SA-ST-PG-X032 marksL2 StandardNon-calculatorMoments
G(t)=12(t+t2)G(t)=\frac12(t+t^2). Find E(X)E(X).

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Salam Academy Original Practice · Proposed mark scheme
SA-ST-PG-X052 marksL2 StandardNon-calculatorSums
XX and YY are independent, each with PGF 12+12t\frac12+\frac12t. Find P(X+Y=1)P(X+Y=1).

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Salam Academy Original Practice · Proposed mark scheme
SA-ST-PG-X061 markL2 StandardNon-calculatorMoments
X∼Geo(0.25)X\sim\text{Geo}(0.25) has PGF 0.25t1−0.75t\frac{0.25t}{1-0.75t}. Find E(X)E(X).

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Salam Academy Original Practice · Proposed mark scheme
SA-ST-PG-0033 marksL3 ExamNon-calculatorMoments
For G(t)=14(1+2t+t2)G(t)=\frac14(1+2t+t^2), find Var(X)\text{Var}(X).

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Salam Academy Original Practice · Proposed mark scheme
SA-ST-PG-0042 marksL3 ExamNon-calculatorSums
X∼Po(2)X\sim\text{Po}(2) and Y∼Po(3)Y\sim\text{Po}(3) are independent. GX+Y(t)=ek(t−1)G_{X+Y}(t)=e^{k(t-1)}. Find kk.

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Salam Academy Original Practice · Proposed mark scheme
SA-ST-PG-X043 marksL3 ExamNon-calculatorMoments
For G(t)=12(t+t2)G(t)=\frac12(t+t^2), find Var(X)\text{Var}(X).

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Salam Academy Original Practice · Proposed mark scheme