Question

Suppose we are interested in bidding on a piece of land and we know one other bidder is interested.1 The seller announced that the highest bid in excess of $10,000 will be accepted. Assume that the competitor’s bid x is a random variable that is uniformly distributed between $10,000 and $15,000. Suppose you bid $12,000. What is the probability that your bid will be accepted?

Answer 1

Answer:

0.4

Step-by-step explanation:

Given:-

- The uniform distribution parameters are as follows:

                      a = $10,000       b = $15,000

Find:-

Suppose you bid $12,000. What is the probability that your bid will be accepted?

Solution:-

- We will denote a random variable X that defines the bid placed being accepted. The variable X follows a uniform distribution with parameters [a,b].

                                 X ~ U(10,000 , 15,000)

- The probability of $12,000 bid being accepted can be determined by the cdf function of the uniform distribution, while the pmf is as follows:

                                Pmf = 1 / ( b - a )

                                Pmf = 1 / ( 15,000 - 10,000 )

                                Pmf = 1 / ( 5,000 )

                                $cdf = \int\limits^x_a {\frac{1}{5000} } \, dy \\\\cdf = {\frac{y}{5000} }\limits^x_a \\\\P(X$