IB Maths AI HL Ahl 4 14 Hl Random Variable Transformations Topic Practice

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Study AHL 4.14 (HL)—Random variable transformations conceptsOpen the corresponding Concept lesson for explanations, examples and exam connections.

Question 1

[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.

Question (a)

(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 ]

Question (i)

(i)

E(T).

[ 1 ]

Question (ii)

(ii)

Var⁡(T)\quad \operatorname{Var}(T).

[ 2 ]
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