← Maths Extension 1 syllabus

NSWMaths Extension 1

Statistical Analysis (ME-S1)

4 dot points across 4 inquiry questions. Click any dot point for a focused answer with worked past exam questions where available.

What is a Bernoulli trial, and what are its mean and variance?

Define a Bernoulli random variable, compute its mean and variance, and recognise scenarios that fit the model
A focused answer to the HSC Maths Extension 1 dot point on Bernoulli trials. The definition, mean $p$ , variance $p (1 - p)$ , and the role of Bernoulli trials as the building block of the binomial distribution.
6 min answer →

What is the binomial distribution, and what are its mean and variance?

Define the binomial distribution $B(n, p)$ , state its probability mass function, and find its mean $n p$ and variance $n p (1 - p)$
A focused answer to the HSC Maths Extension 1 dot point on the binomial distribution. The pmf $P(X = k) = \binom{n}{k} p^k (1 - p)^{n - k}$ , mean $n p$ , variance $n p (1 - p)$ , and standard situations that fit the model.
7 min answer →

How do we calculate probabilities involving the binomial distribution, including ranges and complements?

Compute exact probabilities for the binomial distribution including $P(X = k)$ , $P(X \le k)$ , $P(X \ge k)$ , and use complementary counting
A focused answer to the HSC Maths Extension 1 dot point on computing binomial probabilities. Exact pmf values, cumulative sums, complements (at least, at most), and standard problem patterns, with worked examples.
7 min answer →

When and how do we use the normal distribution to approximate binomial probabilities?

Use the normal approximation $X \sim N(n p, n p (1 - p))$ to approximate binomial probabilities for large $n$
A focused answer to the HSC Maths Extension 1 dot point on the normal approximation of the binomial. The rule of thumb $n p \ge 5$ and $n(1 - p) \ge 5$ , continuity correction, standardising and computing approximate probabilities, with worked examples.
7 min answer →