Suppose Sam and Jack each separately faces the same exact loss distribution, as follows:

$\backslash$table$[[$Possible Outcomes,PROBABILITY$],[$$$0,0\mathrm{.}98],[$$$4,000,0\mathrm{.}02]]$

Case $1$: What is the standard deviation per person respectively if Sam and Jack do NOT pool risk together?

A$)533$

B$)560$

C$)579$

D$)601$

Case $2$: What is the standard deviation per person respectively if Sam and Jack pool risk together and each pays half whenever the other one experiences a loss?

A$)396$

B$)414$

C$)438$

D$)453$

Case $3$: Suppose Emily has the same loss distribution as Sam and Jack. Emily, Sam and Jack pool risk together and each pays $\frac{1}{3}$ whenever the other one experiences a oss. Which of the following is FALSE?

The expected loss per person of Case $3$ is the same as that of Case $2.$

The standard deviation of the aggregate loss of Case $3$ is lower than that of Case $2.$

The expected aggregate losses of Cases $2$ and $3$ are different.

The expected aggregate loss of Case $3$ is higher than that of Case $2.$