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VICMath MethodsQuick questions
Unit 3
Quick questions on Discrete random variables: VCE Math Methods Unit 3
7short 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 example distribution?Show answer
A spinner is divided into four unequal sectors numbered 1, 2, 3, 4 with respective probabilities $0.2, 0.3, 0.3, 0.2$.
What is expected value of a function of $X$?Show answer
$$E(g(X)) = \sum_{x} g(x) \cdot P(X = x)$$
What is worked example?Show answer
A game pays $\$Y$ where $Y = 10 X - 5$ and $X$ is the spinner above.
What is forgetting that probabilities must sum to 1?Show answer
Solving for an unknown probability in a distribution table almost always starts by setting the sum equal to 1.
What is computing $E ^2$ instead of $E $?Show answer
These are different! $E(X^2)$ uses each $x^2$ times its probability; $[E(X)]^2$ squares the already-computed mean. Variance is the difference between them.
What is adding instead of multiplying for variance under scaling?Show answer
$\mathrm{Var}(2X) = 4 \mathrm{Var}(X)$, not $2 \mathrm{Var}(X)$.
What is off-by-one on cumulative probabilities for integer $X$?Show answer
$P(X < 3) = P(X \leq 2)$, not $P(X \leq 3)$.
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