IB Maths AI HL 4.14 Random variable transformations Question Bank

Practise IB Mathematics HL 4.14 by applying random variable transformations methods to exam-style questions.

Exam points

identify the mathematical structure, variable or representation
select and apply the correct theorem, formula or algorithm
check the result using units, domain, graph or logical reasoning

[Maximum number: 3]

Taylor is playing a computer game in which they shoot at spaceships and battleships. The number of spaceships they hit per minute can be modelled by a Poisson distribution with mean 4.2. The number of battleships they hit per minute can be modelled by a Poisson distribution with a mean of 2.3. Any single hit occurs independently of all others.

(a)

Every spaceship that is hit earns Taylor 3 points and every battleship 5 points. Let T be the total points earned in one minute.

Find

[ 3 ]

(i)

E(T).

[ 1 ]

$\mathrm{E}(T)=3 \times 4.2+5 \times 2.3=24.1$

(ii)

$\quad \operatorname{Var}(T)$ .

[ 2 ]

$\quad \operatorname{Var}(T)=3^{2} \times 4.2+5^{2} \times 2.3=95.3$

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AHL 4.14 (HL)—Random variable transformations question 1

Question (a)

Question (i)

Question (ii)