Mathematical Methods — Question 2

QCAA 2024, Paper 2 · 1 mark

Q2 · 2024 · Technology-activeSimple familiar1 mark

QUESTION 2

Calculate the expected value of a continuous random variable

X

with the probability density function

p(x)=\begin{cases}\frac14x^2,&0\le x\le\sqrt[3]{12}\\0,&\text{otherwise}.\end{cases}

(A)

1.72

(B)

1.15

(C)

1.00

(D)

0.11

ABCD

WORKED SOLUTION

1 mark

ANSWER

A — 1.72

Worked solution

E(X)=\int_0^{\sqrt[3]{12}}x(\frac14x^2)\,dx=\frac1{16}(\sqrt[3]{12})^4\approx1.72

, so option A.

Selects option A.

[1 mark]

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