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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TTanishq
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:
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:
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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