Question

At an oral auction for a lamp, half of all bidders have a value of $50 and half have a value of $70. What is the expected winning bid if there are four bidders?

Answer 1

Let there be a random variable X.

By definition,  

Where E(x) = expectation of x.

And, f(x) = P(X=x)

In the given problem, n = total number of bidders = 4.

And, value of 2 bidders = $50 and the value of other 2 bidders = $70.

Therefore, Probability that $50 will be the winning bet = 2/4 = 1/2.

And, probability that $70 will be the winning bet = 2/4 = 1/2.

Expected winning bid = (50*1/2) + (70*1/2)

= 25+35 = 60.

Thus, the expected winning bid of there are four bidders will be $60.