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An individual who has automobile insurance from a certain company is randomly selected. Let Y be the number of moving violations for which the individual was cited during the last 3 years. The pmf of Y is the following.

y 0 1 2 3
p(y) 0.50 0.25 0.20 0.05

(a) Compute E(Y).
(b) Suppose an individual with Y violations incurs a surcharge of $100Y2. Calculate the expected amount of the surcharge.

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opudodennis

Answer:

a. 0.80

b. $80

Step-by-step explanation:

a. The expected value, E(Y) is the sum of: [(each of the possible outcomes) × (the probability of the outcome occurring)]. In more concrete terms, the expectation is what you would expect the outcome of an experiment to be on average:

[tex]E(Y)=S_yP(Y=y)\\\\=0\times 0.5+1\times 0.25+2\times 0.20+3\times 0.05\\\\=0.80[/tex]

Hence the expected value E(Y) is 0.80

b. From a above we have the expectation as  E(Y)=0.80.

-The expected amount is calculated by multiplying  expectation by the surcharge:

[tex]Ex \ Amount= E(Y)\times surcharge\\\\=0.80\times 100\\\\=80[/tex]

Hence, the expected amount of surcharge is $80

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