Consider that Emily and Samantha face the same probability distribution for losses. Assume their claims are independent. The loss distribution is Loss amount. probability 0 1000 4000 7 .2 .1 a. Calculate Emily's expected loss and variance b. If Emily and Samantha form a pool in which losses are shared equally, calculate the expected loss per person, and the expected variance in losses per person. (hint: you first have to calculate the possible loss outcomes in the pool, divide by 2 to get the losses per person, and calculate the associated probabilities.) c. What happened to expected losses per person and variance in losses per person when the pool was formed?