Assume that there are 9 bidders with reservation prices independently and uniformly distributed between $100,000 and $180,000. What is the expected value of the highest reservation price of the nine potential buyers?
A) $140,000
B) $160,000
C) $164,000
D) $172,000
E) $175,000

Question

Quizplus · Accepted Answer

The distribution of the highest reservation price of the nine potential buyers follows the distribution of the maximum value of a sample of size 9 from a uniform distribution between $100,000 and $180,000. 
The expected value of the maximum value of a sample of size n from a uniform distribution between a and b is given by:
$E(X_{max})=b-\frac{b-a}{n+1}$
In this case, a = $100,000$, b = $180,000$, and n = 9. 
So, $E(X_{max})=180,000-\frac{80,000}{10}=172,000$
Therefore, the expected value of the highest reservation price of the nine potential buyers is $172,000. The best choice is D.

Assume That There Are 9 Bidders with Reservation Prices Independently