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

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Uniform Distribution
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What is the continuous uniform distribution also called?

Rectangular distribution

For a continuous uniform distribution over [a,b][a, b], what is the PDF f(x)f(x)?

f(x)=1b−af(x) = \frac{1}{b-a}

What is E(X)E(X) for a continuous uniform distribution over [a,b][a, b]?

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

What is Var(X)\text{Var}(X) for a continuous uniform distribution over [a,b][a, b]?

112(b−a)2\frac{1}{12}(b - a)^2

If XX is uniformly distributed over [−2,7][-2, 7], what is f(x)f(x)?

19\frac{1}{9}

What does X∼U(6)X \sim U(6) represent in discrete uniform distribution?

6 equally likely outcomes

For a discrete uniform distribution X∼U(n)X \sim U(n), what is E(X)E(X)?

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

For X∼U(n)X \sim U(n), what is Var(X)\text{Var}(X)?

112(n2−1)\frac{1}{12}(n^2 - 1)

If E(X)=2E(X) = 2, what is E(3X+4)E(3X + 4)?

1010

If Var(X)=2\text{Var}(X) = 2, what is Var(3X+4)\text{Var}(3X + 4)?

1818

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