Note that 
Answer:
Mary's risk premium is $0.9375
Step-by-step explanation:
Mary's utility function,
Mary's initial wealth = $100
The gamble has a 50% probability of raising her wealth to $115 and a 50% probability of lowering it to $77
Expected wealth of Mary, 
= (0.5 * $115) + (0.5 * $77)
= 57.5 + 38.5
= $96
The expected value of Mary's wealth is $96
Calculate the expected utility (EU) of Mary:-
![E_u = [0.5 * U(115)] + [0.5 * U(77)]\\E_u = [0.5 * 115^{0.5}] + [0.5 * 77^{0.5}]\\E_u = 5.36 + 4.39\\E_u = \$ 9.75](https://tex.z-dn.net/?f=E_u%20%3D%20%5B0.5%20%2A%20U%28115%29%5D%20%2B%20%5B0.5%20%2A%20U%2877%29%5D%5C%5CE_u%20%3D%20%5B0.5%20%2A%20115%5E%7B0.5%7D%5D%20%2B%20%5B0.5%20%2A%2077%5E%7B0.5%7D%5D%5C%5CE_u%20%3D%205.36%20%2B%204.39%5C%5CE_u%20%3D%20%5C%24%209.75)
The expected utility of Mary is $9.75
Mary will be willing to pay an amount P as risk premium to avoid taking the risk, where
U(EW - P) is equal to Mary's expected utility from the risky gamble.
U(EW - P) = EU
U(94 - P) = 9.63
Square root (94 - P) = 9.63
If Mary's risk premium is P, the expected utility will be given by the formula:
Mary's risk premium is $0.9375
You want to distribute and then combine the like terms, as per order of operations. Start by multiplying the 2 by -n and -3, so you get -2n-6. Then distribute the -7 to the 5 and 2n, so you get -35-14n. Combine your n’s and constants, and get -16n-41
Answer:
x = 45
Step-by-step explanation:
x + 135 = 180 {Linear pair}
x = 180 - 135 {Subtract 135 from both sides}
x = 45
Answer:
(4,5)
Step-by-step explanation:
To find the x coordinate of the midpoint, average the x coordinates of the endpoints
(1+7)/2 = 8/2 = 4
To find the y coordinate of the midpoint, average the y coordinates of the endpoints
(2+8)/2 = 10/2 = 5
Step-by-step explanation:
If the vector CD is a multiple of the vector BC
(CD = kBC, where k is a real constant
and k =/= 0),
Then BCD is a straight line.
Vector BC = Vector BA - Vector CA
= (5a - 2b) - (3a + b) = (2a - 3b).
Vector CD = Vector CA + Vector AD
= (3a + b) + (3a - 10b) = (6a - 9b)
Since 3(2a - 3b) = (6a - 9b), => k = 3,
The points B, C and D are collinear.
Hence we conclude BCD is a straight line.
