Financial Risk Manager Part 1
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Living in a certain city is really expensive. The mean spent by a citizen monthly is $3,000 with a variance of $500. Nonetheless, the city mayor decided to put a tax in order to make people regulate their monthly expenses adding 20% to all daily living articles. Find the new variance of this city.
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Community
TTanishq
A
520
B
580
C
600
D
720
Explanation:
Explanation
For this exercise, we need to find the variance of new living costs. Let X be the old living costs and Y the new living costs, then we have:
Y = 1.2X
Var(Y) = Var(1.2X)
= 1.44 Var(X)
= 1.44(500) = 720
Y = 1.2X
Var(Y) = Var(1.2X)
= 1.44 Var(X)
= 1.44(500) = 720
Key Concept: When a random variable is multiplied by a constant, the variance is multiplied by the square of that constant. This is expressed as:
Var(aX) = a²Var(X)
Where:
a = 1.2(20% increase)Var(X) = 500(original variance)Var(Y) = (1.2)² × 500 = 1.44 × 500 = 720
Note that the mean ($3,000) is not needed for calculating the variance, as variance measures spread around the mean, not the mean itself.
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