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Mathematical Methods — Question 7

QCAA 2023, Paper 1 · 1 mark

Q7 · 2023 · Technology-freeSimple familiar1 mark

QUESTION 7

A random variable has probability density function

f(x)=\frac{x}{8}

for

0\le x\le4

. Its mean is

(A)

\frac18

(B)

\frac38

(C)

\frac12

(D)

\frac83

ABCD

Question linkOriginal paper

WORKED SOLUTION

Answer D

1 mark

ANSWER

D —

\frac83

Worked solution

E(X)=\int_0^4 x(x/8)dx=[x^3/24]_0^4=8/3

; D.

Selects option D.

[1 mark]

Worked explanation by QCE Vault; correct option verified against the QCAA answer key.

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