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.

definition: a circle is the  set of all points in a plane that are equidistant  from a given  point  called the center of the circle. we use the symbol ⊙ to represent a circle. the a line segment from the center of the circle to  any point  on the circle is a radius of the circle.

step-by-step explanation:

i googled it and this is what i got i don't know how it is. sorry.

on monday rodney ate 1/4th of the sandwich = 3/12

on tuesday he ate 1/3rd of the sandwich = 4/12

therefore in total he has eaten = 3/12 + 4/12 = 7/12

thus we can say that he has eaten 7/12 of the sandwich on monday and tuesday alltogether.

happy to

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