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VICMath MethodsQuick questions
Unit 2
Quick questions on Bernoulli trials, sample data and simulation: VCE Math Methods Unit 2 Year 11
15short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.
What is being simulated (a Bernoulli trial with $p$ specified)?Show answer
2. Choose a random source. Calculator RAND, coin, dice. 3.
What is procedure?Show answer
1. Define the model. What is being simulated (a Bernoulli trial with $p$ specified)? 2. Choose a random source. Calculator RAND, coin, dice.
What is worked example. Simulating a free throw?Show answer
A basketball player has free-throw probability $p = 0.7$. Simulate 100 trials.
What is why simulation matters?Show answer
Simulation is the practical approach when:
What is mean?Show answer
Sum of values divided by the number of values. Measures the centre.
What is median?Show answer
The middle value when data are ordered. Robust to outliers.
What is mode?Show answer
The most frequent value.
What is range?Show answer
Maximum minus minimum.
What is standard deviation?Show answer
Measures the spread (Unit 3 / 4 will formalise).
What is law of large numbers?Show answer
As $n$ grows, the observed relative frequency tends to the theoretical probability.
What is treating non-independent trials as independent?Show answer
Bernoulli sequences assume each trial is independent. Drawing without replacement, where the sample changes, is not a Bernoulli sequence.
What is confusing $p$ and $1 - p$?Show answer
$p$ is the success probability; $1 - p$ is the failure probability. Both appear in the binomial formula.
What is missing the binomial coefficient?Show answer
$P(\text{exactly } k \text{ successes}) = \binom{n}{k} p^k (1-p)^{n-k}$. The $\binom{n}{k}$ counts arrangements; without it you have only one specific sequence.
What is confusing observed and theoretical?Show answer
$p$ is fixed (theoretical). $\hat p$ is observed (from data) and varies sample to sample.
What is simulation with too few trials?Show answer
Small $n$ gives unreliable estimates. The agreement improves as $\sqrt{n}$.