uppose that Mary's utility function is U(W) = W0.5, where W is wealth. She has an initial wealth of $100. How much of a risk premium would she want to participate in a gamble that has a 50% probability of raising her wealth to $115 and a 50% probability of lowering her wealth to $77? Mary's risk premium is $ nothing. (round your answer to two decimal places)

Note that

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:-

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 can use a^2+ b^2=c^2

there is only one way to arrange all the eight relative to each other because they are not distinct. we have

now there are nine places to place an (and not more than one in one place).   because we have four symbols, we need to choose four of these nine places to insert an . order does not matter because the are not distinct.

thus there are 1 · c(9,4) ways, or, if we calculate it,

thus there are 126 ways to form such "words."