∫VCE Maths Practice

Practice Progress Season Pass

VCE® is a registered trademark of the Victorian Curriculum and Assessment Authority (VCAA). The VCAA does not endorse or make any warranties regarding this study resource.

Past VCAA examination questions are © VCAA. Hints, practice questions and worked solutions are © VCE Maths Practice.

Methods2023 Exam 2 Section A · Q12CAS active1 mark

Maximum mean of a discrete random variable with parameter k

Get help with this question with a Mathematical Methods Season Pass

Step-by-step hints
Instant answer checking
Worked solutions, VCAA-style marks

Unlock with Season Pass

The probability mass function for the discrete random variable $X$ is shown below.

| $X$ | $-1$ | $0$ | $1$ | $2$ | |---|---|---|---|---| | | | | | |

The maximum possible value for the mean of $X$ is:

1 mark

A

0

B

\frac{1}{3}

C

\frac{2}{3}

D

1

E

2

Hints, answer checking and worked solutions come with a Season Pass.

\Pr(X = x)

Pr (X = x)

k^2

-1

k

-k^2 - 4k + 1

Table of the probability mass function: X takes values -1, 0, 1, 2 with probabilities k squared, 3k, k, and negative k squared minus 4k plus 1 respectively.