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.
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A
$8,500
B
$4,250
C
$500
D
$10,500
Explanation:
Explanation
To compute the bonus, we apply the following linear transformation to each employee's salary:
[ Y = \alpha + \beta X ] [ Y = 1,000 + 0.15X ]
where:
- Y is the transformed variable (bonus)
- X is the original variable (salary)
- β is the scale constant (0.15)
- α is the shift constant ($1,000)
The mean bonus, i.e., mean of Y, is given by:
[ E(Y) = E(\alpha + \beta X) = \alpha + \beta E(X) ]
We know that the mean salary is $50,000. Thus:
[ E(Y) = $1,000 + 0.15($50,000) ] [ E(Y) = $1,000 + $7,500 ] [ E(Y) = $8,500 ]
Therefore, the mean bonus received by employees is $8,500.
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