You are the only bidder in an online auction of a nintendo wii system with games and accessories. The seller has set a secret reserve price (the minimum price she is willing to accept for the wii). Assume that the secret reserve price x is uniformally distributed between $240 and $320.1) Height of the probability density function f(x) varies with x as follows (round to four decimal places). 240 ≥ x ≥ 3202) You enter a bid of $280 for the wii. What is the probability that you'll win the auction?3) What is the mean secret reserve price?4) What is the standard deviation of the above question?5) You enter your bid of $280 and see that the seller's reserve price has not been met. You enter a new bit of $300. Now what is the probability that you'll win the auction?

Answer:

1. 1/80 = 0.0125

2. 1/2 = 0.5

3. 280

4. 23.09

5. 1/2 = 0.5

Step-by-step explanation:

1. height of probability density function

[tex]\frac{1}{320-240} \\= \frac{1}{80}[/tex]

= 0.0125

2. probabilty that you will win the auction given a bid of 280

= [tex]\frac{280-240}{320-240} \\=\frac{40}{80} \\= \frac{1}{2}[/tex]

3. mean secret service price

[tex]\frac{320+240}{2} \\=\frac{560}{2} \\= 280[/tex]

4. the standard deviation of the above

= (320-240)/12^1/2

= 23.09

5. with a new bid of 300 dollars, probability you will win auction

= [(300-280)/(320-240)]/[(320-280)/(320-240)

= (20/80) / (40 /80)

= 0.25/0.5

= 0.5

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