2025 HSC Mathematics Extension 1
Question 4:
Binomial distribution
A Bernoulli random variable has probability distribution for . What are the mean and variance of ?
How to recognise this question
Question type: binomial distribution
- The command and notation point to binomial distribution.
- The requested response is a multiple choice.
How to handle it: identify the random variable and its parameters before using the matching probability formula.
Watch out: Do not select a formula until its domain, interval, sign and units match the question.
Step-by-step answer
- and , so this is Bernoulli with .
- .
- Use .
- , so option C is correct.
Common mistake: choosing a familiar formula before checking that its conditions, signs, interval and units match this question.
The paper records 1 total mark for this group. Where the official marking guide provides useful partial-credit criteria, those criteria are stated in the steps above.
Try your hand at it again by answering these questions
Question 1
A Bernoulli random variable has and . What are the mean and variance of ?
Question 2
A Bernoulli random variable has and . What are the mean and variance of ?
Question 3
A random variable takes the values and , with . What are the mean and variance of ?