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?

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) = aThe 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) = 0The 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.

answer:

1. 0.04

2. 0.15

step-by-step explanation:

i just finished that assignment for properties of probability distributions.

mr. flanders’ class sold 47 doughnuts and   mr. rodriquez’s class sold 38 cartons of milk

step-by-step explanation:

let x be the number of doughnuts sold by mr. flanders’ class and y be the number of cartons sold by mr. rodriquez’s class.

1. together, the classes sold 85 items, then

x+y=85.

2. both classes earn earned $104.49 for their school. if doughnuts were sold for $1.35 each, then x doughnuts costed $1.35x. if cartons of milk were sold for $1.08 each, then y cartons costed $1.08y. hence,

1.35x+1.08y=104.49.

3. solve the system of two equations: