Carl decides to sell his old laptop on eBay, and sequentially receives bids from potential buyers. The minimum price that he will accept to sell his laptop for is $600. Let {Xn, n ≥ 0} denote the sequence of independent and identically distributed bids that Carl receives, and assume that each Xn has the following probability density function fX (x) = (1/400)e −x/400 for x ≥ 0. Let N denote the number of bids that Carl obtains before selling his laptop i.e., Carl sells his laptop to the Nth bid. (a) Find E[N]. (b)Find E[XN ].

Carl decides to sell his old laptop on eBay, and sequentially receives bids from potential buyers. The minimum price that he will accept to sell his laptop for is $600. Let {Xn, n ≥ 0} denote the sequence of independent and identically distributed bids that Carl receives, and assume that each Xn has the following probability density function fX (x) = (1/400)e −x/400 for x ≥ 0. Let N denote the number of bids that Carl obtains before selling his laptop i.e., Carl sells his laptop to the Nth bid. (a) Find E[N]. (b)Find E[XN ].

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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Alex decides to sell his old guitar, and sequentially receives bids from potential buyers. The minimum price that he will accept to sell his guitar for is £500. Let {Xn, n ≥ 0} denote the sequence of independent and identically distributed bids that Alex receives, and assume that each Xn has the following probability density functionfX(x) = (1/400)e-x/400 for x ≥ 0. Let N denote the number of bids that Alex obtains before selling his guitar i.e., Alex sells his laptop to the Nth bid. Showing your full working, (a) find E[N]. (b) find E[XN].
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