A broker has calculated the expected values of two financial instruments X and Y. Suppose that E (X) = $104, E (Y) = $81, SD (X) = $12 and SD (Y) = $10. Find each of the following. a) E (X + 10) and SD (X + 10) b) E (5Y) and SD (5Y) c) E (X + Y) and SD (X + Y) d) What assumption must you make in part c?

Question

Amiyah Hood

Mathematics

17 January, 20:17

A broker has calculated the expected values of two financial instruments X and Y. Suppose that E (X) = $104, E (Y) = $81, SD (X) = $12 and SD (Y) = $10. Find each of the following. a) E (X + 10) and SD (X + 10) b) E (5Y) and SD (5Y) c) E (X + Y) and SD (X + Y) d) What assumption must you make in part c?

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Answers (1)

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Kira Guzman · Answer 1

a) E (X + 10) and SD (X + 10)

E (X + 10) = $114

SD (X + 10) = $12

b) E (5Y) and SD (5Y)

E (5Y) = $405

SD (5Y) = $50

c) E (X + Y) and SD (X + Y)

E (X+Y) = $185

SD (X + Y) = $15.62

d. See explanation below

Step-by-step explanation:

Given

E (X) = $104

E (Y) = $81

SD (X) = $12

SD (Y) = $10

We'll solve the above questions using this principle:

E (a) = a The mean value of a constant a is a.

E (aX) = a E (X) If each value in a probability distribution is multiplied by a, the mean of the distribution will be multiplied by a factor of a.

E (aX + b) = a E (X) + b

If a constant value, b, is added to or subtracted from each value in a probability distribution, the mean of the distribution will be increased or decreased by b.

SD (a) = 0 The standard deivation value of a constant a is 0.

SD (aX) = a SD (X) If each value in a probability distribution is multiplied by a, the standard deviation of the distribution will be multiplied by a factor of a.

SD (aX + b) = a SD (X)

If a constant value, b, is added to or subtracted from each value in a probability distribution, the standard deviation of the distribution will be unchanged.

where a and b are constants

a) E (X + 10) and SD (X + 10)

E (X + 10)

= E (X) + 10

= $104 + $10

= $114

SD (X + 10)

= SD (X)

= $12

b) E (5Y) and SD (5Y)

E (5Y)

= 5E (Y)

= 5 * $81

= $405

SD (5Y)

= 5SD (Y)

= 5 * $10

= $50

c) E (X + Y) and SD (X + Y)

E (X+Y)

= E (X) + E (Y)

= $104 + $81

= $185

SD (X + Y)

= √ ((SD (X)) ² + (SD (Y) ²)

= √ (12² + 10²)

= √244

= $15.62049935181330

= $15.62

d) What assumption must you make in part c?

order to calculate the standard deviation (variance) in part c), we must assume that the two different financial instruments (X and Y) are independent.