An individual who has automobile insurance from a certain company is randomly selected. Let Y be the number of mov- ing violations for which the individual was cited during the last 3 years. The pmf of Y is y0123 p(y) .60 .25 .10 .05 a. Compute E(Y). b. Suppose an individual with Y violations incurs a sur- charge of $100Y2. Calculate the expected amount of the surcharge

a)

And replacing we got:

b)

And then the expected value would be:

Step-by-step explanation:

We assume the following distribution given:

Y       0       1        2        3

P(Y) 0.60 0.25  0.10  0.05

Part a

We can find the expected value with this formula:

And replacing we got:

Part b

If we want to find the expected value of we need to find the expected value of Y^2 and we have:

And replacing we got:

And then the expected value would be:

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step-by-step explanation: