Answer:
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.