Midterm-Math 526, Fall 2016 Roll a fair die repeatedly and let Y 1 ;Y 2 ;::: be the resulting numbers. Let X n D jfY 1 ;Y 2 ;:::;Y n gj be the number of values we have seen in the first n rolls for n ? 1 and set X 0 D 0. X n is a Markov chain. (a) Find its transition probability. (b) Let T D minfn W X n D 6g be the number of trials we need to see all 6 numbers at least once. Find ET.

An appliance store sells a washer-dryer combination for $1800. if the washer costs $300 more than the dryer, find the cost for each appliance.

Agroup of students want to create a garden. they do not know the exact measurements but they propose using a variable to represent the length and width of the garden. the length of the garden is 10 feet longer than double the width. use a single variable to write algebraic expressions for both the length and width of the garden. write an algebraic expression for the area of the garden. use mathematical terms to describe this expression.

Why is causation so much more difficult to prove than correlation?