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 stay with your bid in part (c); it maximizes expected profit or bid $13,100 to maximize the expected profititem

what is the expected profit for this bid (to 2 decimals)?

$

a. 0.83

b. 0.97

c.$14500 or more

d. stay with bid in part c

e. $4400.00

Step-by-step explanation:

a. the probability that the bid of $12, 000 is accepted=

probability = bid/ Max bid  = $12000/ $14500 =0.83

b. the probability that the bid of $14, 000 is accepted=

probability = bid/ Max bid  = $14000/ $14500 =0.97

c. the maximum bidder get the property, since the bid is in the range of $10100 and $14500, therefore, the bidder with $14500 or more will get the property.

d. if your objective is to maximize expected profit, stay with your bid in part c. which is $14500 or more will get the property.

e. the expected profit will be $14500 -$10100 = $4,400.00

0.4,08,>15000, No

Step-by-step explanation:

Given that 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 $10,000 will be accepted.

Competitor Bid is U (10000,15000)

If your bid is more than competitors bid your bid will be accepted

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

=

b) Suppose you bid $14,000. What is the probability that your bid will be accepted

=

c) amount should you bid to maximize the probability that you get the

property>15000 because the prob to get the bid is

d) Suppose you know someone who is willing to pay you $16,000 for the property. Would  you consider bidding less than the amount in part (c)? Why or why not

No.  Bid for 15000 will allow to win the bid and also get a profit of 1000 dollars by selling immediately.

0.49 = 49% probability that your bid will be accepted

Step-by-step explanation:

An uniform probability is a case of probability in which each outcome is equally as likely.

For this situation, we have a lower limit of the distribution that we call a and an upper limit that we call b.

The probability that we find a value X lower than x is given by the following formula.

Uniformly distributed between $9,600 and $14,500.

This means that

Suppose you bid $12,000. What is the probability that your bid will be accepted (to 2 decimals)?

Your bid will be accepted if the competitor's bid X is lower than 12000. So

0.49 = 49% probability that your bid will be accepted

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 )

And for this case we can use the cumulative distribution function given by:

And using this formula we have this:

Then we can conclude that the probability that your bid will be accepted would be 0.41

Step-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:

If your offer is accepted is because your bid is higher than the others. And we want to find the following probability:

And for this case we can use the cumulative distribution function given by:

And using this formula we have this:

Then we can conclude that the probability that your bid will be accepted would be 0.41

a) 0.32 = 32% probability that your bid will be accepted

b) 0.72 = 72% probability that your bid will be accepted

c) An amount in excess of $15,400.

Step-by-step explanation:

An uniform probability is a case of probability in which each outcome is equally as likely.

For this situation, we have a lower limit of the distribution that we call a and an upper limit that we call b.

The probability that we find a value X lower than x is given by the following formula.

Assume that the competitor's bid x is a random variable that is uniformly distributed between $10,400 and $15,400.

This means that

a. Suppose you bid $12,000. What is the probability that your bid will be accepted (to 2 decimals)?

You will win if the competitor bids less than 12000. So

0.32 = 32% probability that your bid will be accepted

b. Suppose you bid $14,000. What is the probability that your bid will be accepted?

You will win if the competitor bids less than 14000. So

0.72 = 72% probability that your bid will be accepted

c. What amount should you bid to maximize the probability that you get the property (in dollars)?

His bid is uniformly distributed between $10,400 and $15,400.

So, to maximize the probability that you get the property, you should bid an amount in excess of $15,400.

Explanation:

f(x) = (1/(15,000-10,000))/0 (elsewhere) = 1/5000

a. What is the probability that a $12,000 bid will be accepted?

P(10,000 < x < 12,000) = 2000(1/5000) = 0.40

b. What is the probability that a $14,000 bid will be accepted?

P(10,000 < x < 14,000) = 4000(1/5000) = 0.80

c. What amount should you bid to maximize the probability that you get the property?

$14,000 is my answer.

$14000 bid has a higher probability, hence a greater chance of being accepted

P(bid accepted) = 0.4

Step-by-step explanation:

Defining the probability function of the competitor's bid as

for x between 10000 and 15000

We can calculate the probability that our bid of $12,000 is accepted as

Probability (bid accepted) = 0.48

Step-by-step explanation:

Probability density is given byF(y)= 1/(b-a)

a=9500

b= 14700

F(y)= 1/(14700-9500) =1/5200=0.00019

Probability (bid accepted)= (12000-9500)÷1/5200

P( bid accepted) = 2500×0.00019=0.475 approximately 0.48

Step-by-step explanation:

(a)

The bid should be greater than $10,000 to get accepted by the seller. Let bid x be a continuous random variable that is uniformly distributed between

$10,000 and $15,000

The interval of the accepted bidding is , where b = $15000 and a = $10000.

The interval of the provided bidding is [$10,000,$12,000]. The probability is calculated as,

(b)  The interval of the accepted bidding is [$10,000,$15,000], where b = $15,000 and a =$10,000. The interval of the given bidding is [$10,000,$14,000].

(c)

The amount that the customer bid to maximize the probability that the customer is getting the property is calculated as,  

The interval of the accepted bidding is [$10,000,$15,000],

where b = $15,000 and a = $10,000. The interval of the given bidding is [$10,000,$15,000].

(d)  The amount that the customer bid to maximize the probability that the customer is getting the property is $15,000, set by the seller. Another customer is willing to buy the property at $16,000.The bidding less than $16,000 getting considered as the minimum amount to get the property is $10,000.

The bidding amount less than $16,000 considered by the customers as the minimum amount to get the property is $10,000, and greater than $16,000 will depend on how useful the property is for the customer.