Consider the activities for Project Respawn Flash shown in the $($partially incomplete$)$ table below, along with expected times and variances of times. Assume time is measured in hours.

$\backslash$table$[[$ACTIVITY$,$EXPECTED TIME,VARIANCE OF TIME$],[$A$,7,0\mathrm{.}11],[$B$,2,0\mathrm{.}80],[$C$,6,0\mathrm{.}22],[$D$,11,0\mathrm{.}43],[$E$,9,0\mathrm{.}11],[$F$,4,0\mathrm{.}22],[$G$,,],[$H$,6,1\mathrm{.}00]]$

$($A$)$ Suppose the probability distribution for Activity $G$ follows a beta distribution and the the most likely, pessimistic, and optimistic times for the activity are $2,11,$ and $1$ hours respectively. Find the expected time and variance for Activity $G$

Note: In this eample the expected time and variance for each task is Iready calculated for the rest of activities. Remmber we use the following equations to find these two terms:

$t=$ expected time $=\frac{a+4^{**}(m)+b}{6}$

variance $=(\frac{b-a}{6}{)}^{{?}^{{?}^{?}}}2$

$a=$ optimistic time

$b=$ pessimistic time

$m=$ most likely

Inlude two decimal points.

$\backslash$table$[[$A$,7,0\mathrm{.}11],[$B$,2,0\mathrm{.}80],[$C$,6,0\mathrm{.}22],[$D$,11,0\mathrm{.}43],[$E$,9,0\mathrm{.}11],[$F$,4,0\mathrm{.}22],[$G$,,],[H,6,1\mathrm{.}00]]$

$($A$)$ Suppose the probability distribution for Activity $G$ follows a beta distribution and the the most likely, pessimistic, and optimistic times for the activity are $2,11,$ and $1$ hours respectively. Find the expected time and variance for Activity $G$ :

Note: In this eample the expected time and variance for each task is Iready calculated for the rest of activities. Remmber we use the following equations to find these two terms:

$t=$ expected time $=\frac{a+4^{**}(m)+b}{6}$

variance $=(\frac{b-a}{6}{)}^{{?}^{{?}^{?}}}2$

$a=$ optimistic time

$b=$ pessimistic time

$m=$ most likely

Inlude two decimal points.

Answer: Expected time $=$

; Variance $=$