Uniform Distribution (Edexcel A-Level Further Mathematics): Flashcards

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Uniform Distribution
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Alternative name for continuous uniform distribution

Rectangular distribution

PDF of continuous uniform on [a,b][a,b]

f(x)=1b−af(x) = \frac{1}{b-a} for a≤x≤ba \leq x \leq b

E(X)E(X) for continuous uniform on [a,b][a,b]

12(a+b)\frac{1}{2}(a+b)

Var(X)\text{Var}(X) for continuous uniform on [a,b][a,b]

112(b−a)2\frac{1}{12}(b-a)^2

Height of rectangle in continuous uniform [a,b][a,b]

1b−a\frac{1}{b-a}

Notation for discrete uniform with nn outcomes

X∼U(n)X \sim U(n)

E(X)E(X) for X∼U(n)X \sim U(n)

n+12\frac{n+1}{2}

Var(X)\text{Var}(X) for X∼U(n)X \sim U(n)

112(n2−1)\frac{1}{12}(n^2-1)

E(aX+b)E(aX+b) in terms of E(X)E(X)

aE(X)+baE(X) + b

Var(aX+b)\text{Var}(aX+b) in terms of Var(X)\text{Var}(X)

a2Var(X)a^2\text{Var}(X)

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Discrete Probability Distributions

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Discrete Probability Distributions

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Discrete Probability Distributions

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