Let X be the damage incurred (in $) in a certain type of accident during a given year. Possible X values are 0, 1000, 5000, and 10000, with probabilities 0.80, 0.08, 0.10, and 0.02, respectively. A particular company offers three different policies: a $200 deductible with a $780 premium, a $500 deductible with a $700 premium, and a $1000 deductible with a $590 premium. (A $Y deductible means the insurance company pays X - Y for X Y and 0 for X Y.) Compute the expected profit for each policy.

Expected profit policy 1 = $40

Expected profit policy 2 = $20

Expected profit policy 3 = $10

Step-by-step explanation:

X values     |    Probability P(x)

0                 |        0.80

1,000          |        0.08

5,000         |        0.10

10,000       |        0.02

A particular company offers three different policies:

Policy 1: $200 deductible with a $780 premium

Policy 2: $500 deductible with a $700 premium

Policy 3: $1000 deductible with a $590 premium

The company pays  X - Y in damages if X > Y and 0 otherwise.

So the expected profit is given by

Expected profit = Premium amount - Expected payout

Expected profit = Premium amount - [ (X - deductible) × P(x) ]

Expected profit Policy 1:

E(x) = $780 - [ 0×0.80 + (1,000 - 200)×0.08 + (5,000 - 200)×0.10 + (10,000 - 200)×0.02 ]

E(x) = $780 - [ 0 + 64 + 480 + 196 ]

E(x) = $780 - $740

E(x) = $40

Expected profit Policy 2:

E(x) = $700 - [ 0×0.80 + (1,000 - 500)×0.08 + (5,000 - 500)×0.10 + (10,000 - 500)×0.02 ]

E(x) = $700 - [ 0 + 40 + 450 + 190 ]

E(x) = $700 - $680

E(x) = $20

Expected profit Policy 3:

E(x) = $590 - [ 0×0.80 + (1,000 - 1,000)×0.08 + (5,000 - 1,000)×0.10 + (10,000 - 1,000)×0.02 ]

E(x) = $590 - [ 0 + 0 + 400 + 180 ]

E(x) = $590 - $580

E(x) = $10

Therefore, the expected profits for the three policies are:

Expected profit policy 1 = $40

Expected profit policy 2 = $20

Expected profit policy 3 = $10

answer: median

step-by-step explanation:

the median is the middle value when a data set is ordered from least to greatest

step-by-step explanation:

one of the most important purposes of surface treatment is to alter surface properties according to the requirement of specific applications. for example, hydrophobic coating has been utilized on windshield and eyeglasses. gold atom monolayer on substrate has become a popular surface bioconjugation strategy.