Question

1. consider a lottery with three possible outcomes: $125 will be received with probability 0.25, $100 will be received with probability 0.3 and $50 will be received with probability 0.45. a. what is the expected value of the lottery? b. what is the variance of the outcome? c. what would a risk-neutral person pay (at most) to play the lottery?

Answer 1

Answer:

Step-by-step explanation:

Expected value of the lottery is $83.75.

Variance of the outcome is 909.6.

A risk-neutral person would pay $83.75 or less to play the lottery.

a) The expected value is obtained by multiplying each result by its likelihood.

The expected value of the lottery is then calculated by adding up all of these.

This is,

125(0.25) + 100(0.3) + 50(0.45)

          = $83.75

b) we can calculate the variance as follows:

Variance=.25*(125-83.75)^2+.3*(100-83.75)^2+.45*(50-80)^2=909.6

c) A risk-neutral person would pay $83.75 or less to play the lottery.

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Answer 2

The lottery's anticipated worth is $80.

Given that,

The probability of receiving $125 is 0.25; the likelihood of receiving $100 is 0.3; and the likelihood of receiving $50 is 0.45.

A) EV=125*.2+100*.3+50*.5=$80

The lottery's anticipated worth is $80.

The expected value is obtained by multiplying each result by its likelihood.

The expected value of the lottery is then calculated by adding up all of these.

This is what we have: ;;

125(0.2) + 100(0.3) + 50(0.5) (0.5)

= 25 + 30 + 25 = $80

B) This is the formula for variance is shown in figure :

So, we can calculate the variance as follows:

.2*(125-80)^2+.3*(100-80)^2+.5*(50-80)^2=975

C) A risk-neutral person would pay $80 or less to play the lottery.

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