Independent solution

How to solve this Expected Value question

Setup

Setup

List the payment associated with each of the five possible outcomes. The outcome probabilities are proportional to five, four, three, two, and one.

b(k)=(100,200,300,350,400)for k=1,…,5b(k)=(100,200,300,350,400)\quad\text{for }k=1,\ldots,5

Model

Model

The expected payment is the probability-weighted sum of the five payment amounts.

E[b(X)]=115{5(100)+4(200)+3(300)+2(350)+1(400)}E[b(X)]=\frac1{15}\{5(100)+4(200)+3(300)+2(350)+1(400)\}

Compute

Compute

The weighted numerator is 3,300 and the probability denominator is 15, giving expected payment 220.

E[b(X)]=3300/15=220E[b(X)]=3300/15=220

Answer

Answer

The expected payment is 220, selecting choice C.

220(C)\boxed{220\quad\text{(C)}}