A dart is thrown at a number line in such a way that it always lands in the interval [0,10]. Let x represent the number that the dart hits. Suppose that the probability density function for x is given by the following function.1f(x) = 50x, for 0≤x≤ 10Find P(6 ≤x≤ 10), the probability that the dart lands in [6,10].How is the probability that the dart lands in [6,10] found?1O A. Integrate 50x twice, then evaluate the integral over the limits 6 and 10.1O B. Evaluate the expression 50x over the limits 6 and 10, then subtract.1OC. Evaluate the expression over the limits 6 and 10, then add.1ⒸD. Integrate 50x, then evaluate the integral over the limits 6 and 10.P(6≤x≤ 10) = (Type an integer or a simplified fraction.)C

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Answered: A dart is thrown at a number line in…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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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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