Financial Risk Manager Part 1
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The average salary for an employee at Capital Asset Managers is $50,000 per year. This year, the management has decided to award bonuses to every employee:
- A Christmas bonus of
$1,000 - An incentive bonus equal to 15% of the employee's salary
Determine the mean bonus received by employees.
Other
Community
NNikitesh
A
$8,500
B
$4,250
C
$500
D
$10,500
Explanation:
To compute the bonus, we apply the following linear transformation to each employee's salary:
Y = α + βx
Y = 1,000 + 0.15x
Y = α + βx
Y = 1,000 + 0.15x
where Y is the transformed variable (bonus), X is the original variable (salary), β is the scale constant, and α is the shift constant.
The mean bonus, i.e., mean of Y, is given by:
E(Y) = E(α + βx) = α + βE(X)
E(Y) = E(α + βx) = α + βE(X)
We know that the mean salary is $50,000. Thus,
E(Y) = `$1`,000 + 0.15(`$50`,000) = `$8`,500
E(Y) = `$1`,000 + 0.15(`$50`,000) = `$8`,500
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