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Mathematical Methods — Question 10

QCAA 2023, Paper 1 · 1 mark

Q10 · 2023 · Technology-freeSimple familiar1 mark

QUESTION 10

A random variable has probability density function

f(y)=1+y

for

0\le y\le\sqrt3-1

. Determine

P(0\le Y\le\frac12)

.

(A)

\frac15

(B)

\frac38

(C)

\frac58

(D)

\frac34

ABCD

Question linkOriginal paper

WORKED SOLUTION

Answer C

1 mark

ANSWER

C —

\frac58

Worked solution

P(Y\le1/2)=\int_0^{1/2}(1+y)dy=1/2+1/8=5/8

; C.

Selects option C.

[1 mark]

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

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