01

(1) Express in terms of .


(2) Compute .


(3) State formula for finding the PDF of .


(4) State PDF for .


(5) Compute PDF for using the formula.

02

(1) Recall the definition of .


(2) Use -substitution to simplify the integral.

Let

Change the bounds, and .


(3) Recall that integrating a PDF from to yields .

03

(a)

(1) Write desired probability in terms of values.


(2) Evaluate using a value table.


(b)

(1) Use the value table to find if


(2) Solve for knowing that .


(c)

Recall formula for and solve for

Plug in for and for and compute .

04

(a)

(1) Write desired probability in terms of values.


(2) Use table to evaluate expression.


(b)

(1) Interpret problem.

Since we wish to find the top , we wish to find such that .


(2) Use lookup table to find .


(3) Given that , solve for .


(c)

(1) Interpret problem.

Since we wish to find the 25th percentile, we wish to find such that .


(2) Use lookup table to find .


(3) Given that , solve for .

06

(1) Find PDF of .

If , insurance covers 0$.

If , then the insurance covers dollars.


(2) Integrate to find .

Since the cost of repairs in uniformly distributed, we have , .

07

08

(a)

(b)

09

Case 1:

Case 2:

Therefore:

10

Case 1:

Case 2:

Therefore: