Mathematical Methods — Question 8

QCAA 2021, Paper 1 · 1 mark

Q8 · 2021 · Technology-freeSimple familiar1 mark

QUESTION 8

The continuous random variable

X

has the probability density function

f(x)=\begin{cases}\dfrac{3}{x^2},&1\le x\le\dfrac32,\\0,&\text{otherwise.}\end{cases}

The mean of

X

(A)

\ln\left(\frac32\right)

(B)

\ln\left(\frac{27}{8}\right)

(C)

\ln\left(\frac92\right)

(D)

ABCD

WORKED SOLUTION

1 mark

ANSWER

Worked solution

E(X)=\int_1^{3/2}x(3/x^2)dx=3\ln(3/2)=\ln((3/2)^3)=\ln(27/8)

Selects option B.

[1 mark]

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