The data matrix below indicates which of $9$ different outdoor activities $($e$.$g$.,$ snowboarding, hiking, etc.$)4$

randomly sampled individuals in Burlington have engaged in at least once over the past year. A

researcher wants to calculate the similarity of outdoor activities for each pair of individuals $($for input

into a cluster analysis$),$ i$.$e$.,$ for pairs of individuals AB$,$ AC$,$ AD$,$ BC$,$ BD$,$ and CD$?$

Attribute: outdoor activity

Individual $123456789$

A $001110001$

B $111010110$

C $011001001$

D $110001111$

In the matrix, a $1$ indicates that the individual has participated in the activity, and a $0$ indicates that s$/$he

has not.

Let: a $=$ # of positive matches between any pair $($i$,$j$)$ of individuals $($i$.$e$.,$ i$=1,$ j$=1)$

b $=$ # of negative matches between any pair $($i$,$j$)$ of individuals $($i$.$e$.,$ i$=0,$ j$=0)$

c $=$ # of i$=1,$ j$=0$ mismatches between any pair of individuals

d $=$ # of i$=0,$ j$=1$ mismatches between any pair of individuals

Additionally, let:

$+$

$+++=$matching$($or similarity$)$ coefficient $$Alpha$$

$$

$++=$matching$($or similarity$)$ coefficient $$Beta$$

$(1)$ Using matching coefficient Alpha, what is the outdoor activity $$similarity$$ coefficient for the

following pair of individuals? $($Provide answer in decimal form, to $4$ places, e$.$g$.,0\mathrm{.}1234)$

AC similarity coefficient $=\_\_\_\_\_\_\_\_\_\_\_\_$

$(2)$ Using matching coefficient Beta, what is the outdoor activity $$similarity$$ coefficient for the following

pair of individuals?

BD similarity coefficient $=\_\_\_\_\_\_\_\_\_\_\_\_\_$