MATH SOLVE

2 months ago

Q:
# Suppose we are interested in bidding on a piece of land and we know one other bidder is interested. The seller announced that the highest bid in excess of $10,100 will be accepted. Assume that the competitor's bid x is a random variable that is uniformly distributed between $10,100 and $14,500. a. Suppose you bid $12,000. What is the probability that your bid will be accepted (to 2 decimals)?_____________b. Suppose you bid $14,000. What is the probability that your bid will be accepted (to 2 decimals)?_____________c. What amount should you bid to maximize the probability that you get the property?$ _____________d. Suppose that you know someone is willing to pay you $16,000 for the property. You are considering bidding the amount shown in part (c) but a friend suggests you bid $13,100. If your objective is to maximize the expected profit, what is your bid?- Select your answer: Stay with your bid in part (c); it maximizes expected profit or Bid $13,100 to maximize the expected profitItemWhat is the expected profit for this bid (to 2 decimals)?$ _____________

Accepted Solution

A:

Answer:[tex] P(X<12000)[/tex]And for this case we can use the cumulative distribution function given by:[tex] P(X\leq x) =\frac{x-a}{b-a}, a \leq x \leq b[/tex]And using this formula we have this:[tex] P(X<12000)= \frac{12000-10100}{14700-10100}= 0.41[/tex]Then we can conclude that the probability that your bid will be accepted would be 0.41Step-by-step explanation:Let X the random variable of interest "the bid offered" and we know that the distribution for this random variable is given by:[tex] X \sim Unif( a= 10100, b =14700)[/tex]If your offer is accepted is because your bid is higher than the others. And we want to find the following probability:[tex] P(X<12000)[/tex]And for this case we can use the cumulative distribution function given by:[tex] P(X\leq x) =\frac{x-a}{b-a}, a \leq x \leq b[/tex]And using this formula we have this:[tex] P(X<12000)= \frac{12000-10100}{14700-10100}= 0.41[/tex]Then we can conclude that the probability that your bid will be accepted would be 0.41