=Question 2 Consider a standard auction setting with two bidders (i = 1,2). Let F₁(v) :√ where v € [0, 1] the cumulative distribution which bidder 1's valuation is drawn from(and f₁ = v¯ the corresponding density function). Let F2(v) v² where v € [0, 2]the cumulative distribution which bidder 2's valuation is drawn from (and ƒ2 = ¹⁄v thecorresponding density function).=Consider Second price sealed auction.(a) Is bidding one's own valuation a weakly dominant strategy for bidder 1? Explainwhy/why not.(b) Is bidding one's own valuation a weakly dominant strategy for bidder 2? Explainwhy/why not.(c) What is the expected payment of bidder 1?(d) What is the expected payment of bidder 2?

(a) Bidding one's own valuation is not a weakly dominant strategy for bidder 1. To see why, suppose…

Answered: Question 2 Consider a standard auction…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Example 3: The probability density ƒ(x) of a continuous random variable is given by f(x) 3 ce , -m
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Suppose Y, and Y, are random variables with joint pdf fy,x, (V1,Y2) = S6(1 – y2), 0, 0 < y1 < y2 otherwise Let U1 =4 and U2 = Y,. Use the transformation technique to show that Ui follows a uniform %3D distribution from 0 to 1.
3. Let X; N iid U(0, 1) for i e {1, 2, ...,n}. (a) Compute the pdf of Y; = - log(X;), name the distribution that Y; follows and provide any parameter value or values needed. (b) Compute the pdf that W = [I", X, = X1 X2... X, follows. You may use the result given as part of the Example 2.6 video (even though it will only be proved in Chapter 3). (c) Compute E[W] in the two following ways: (i) through exploiting independence of the X, and using EUV] = E[U]E[V] for any independent random variables U and V. (ii) using the pdf of W computed in the previous part.
Let X1,., Xn all be independent exponential distributions all with the same parameter 2. What is the distribution of the minimum of (X1,. a) what is the distribution of the smallest order statistic Y, ? b) Specify both the pdf of the distribution and describe the distribution and its parameters. ,Xn)? In other words:
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Let X; € {1,2, 3, ...} be the number of days until relapse for patient i who is diagnosed with multiple sclerosis and currently in remission. We model this data using a geometric distribution with pmf iid X1, X2,..., Xn fxp(x | p) = (1 – p)*-'p for 0 < p < 1 defined on x E {1,2, 3, ...} and 0 elsewhere. Here, p is the risk of relapse on each day. 1. Using a p~ Beta(a, B) prior, derive the posterior density of p, fp|X, (p | Xn).
2.Suppose that the return R (in dollars per share) of a stock has the uniform distribution on the interval [-3,7]. Suppose also, that each share of the stock costs $1.50. Let Y be the net return (total return minus cost) on an investment of 10 shares of the stocks. Compute E(Y).
Derive the following:(c) variance(d) moment generating function

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