Combinations of random variables

WST03Topic 3.12 questions

Distributions of linear combinations of independent Normal random variables.

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Original practice questions written in the style of the exam.

∼

N(900,600)

M1 Standardises:

z = \dfrac{930 - 900}{\sqrt{600}} = 1.22

(1)

A1

P(T > 930) = 0.110

(awrt

0.11

) (1)

M1

D = B_1 + B_2 - A

with mean

160 - 150 = 10

(1)

A1

\operatorname{Var}(D) = 36 + 36 + 100 = 172

(1)

A1

P(D > 0) = P\left(Z > -\dfrac{10}{\sqrt{172}}\right) = P(Z < 0.762) = 0.777

(awrt

0.777

) (1)