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:

the smallest possible measurement of the width is 14 feet

step-by-step explanation:

let's assume length of parallelogram is 'l'

width of parallelogram is 'w'

the perimeter of a parallelogram must be no less than 40 feet

so, we get

we are given

length of parallelogram is 6 feet

so,

l=6

we can plug it

now, we can solve for w

subtract both sides by 12

divide both sides by 2

and we get

so,

the smallest possible measurement of the width is 14 feet