An individual who has automobile insurance from acertain company is randomly selected. Let Y be thenumber of moving violations for which the individualwas cited during the last 3 years. The pmf of Y is y p(y) 0 0.6 1 0.25 2 0.10 3 0.05 Suppose an individual with Y violations incurs a surcharge of $ 100 Y squared. Calculate the expected amount of the surcharge.

And we have that :

And replacing we got:

And finally we have:

Step-by-step explanation:

For this case we have the following probability masss function given:

Y         0           1              2             3

p(Y)    0.6        0.25      0.10         0.05

And we can define the surcharge with this expression

We want to find the expected value for the last expression and we can do it on this way:

And we have that :

And replacing we got:

And finally we have:

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step-by-step explanation:

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