2. The uniform distribution You are the only bidder in an online auction of a Ni

Question

2. The uniform distribution You are the only bidder in an online auction of a Nintendo Wii system bundled 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 uniformly distributed between $200 and $400 Use the Distributions tool to help you answer the questions that follow Uniform 0100 Minimum = 200 0075 Maximum = 400 0050 0025 200 220 240 260 280 300 320 340 360 380 400 The height of the graph of the probability density function f(x) varies with x as follows (round to four decimal places): Height of the Graph of the Probability Density Function X 400

Explanation / Answer

here height or pdf f(x) =1/(b-a) =1/(400-200)=0.005

probability to win for $250 =P(X<250) =(250-200)/200 =0.25

mean secret reserve price =(a+b)/2 =300 and std deviaiton =(b-a)/(12)1/2=57.535

P(X<300|X>250) =(300-250)/(400-250) =50/150 =0.3333

interquartile range =(Q3-Q1) =350-250 =100

x height x<200 0 200<=x<=400 0.005 x>400 0

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