a group of people are having a charity fair by having a lottery. Every participant can win in three idependent rounds. The chance og winning in every round are different. the probability to win in round 1 is θ, round 2: 4θ, and round 3: 5θ. θ <max(1/4, 1/5). in round 2 and three does every participant have the chance to win regardless of prevoius wins. X1, X2, and X3 determine if you win. Xj = 1 if you win, if not 0. You want to estimte the probabililty θ from the three observations. X1, X2 and X3 with the following estiamtions (picture) Show that both estimates are right of expectation. Find an expression for the variance to ˆθ1 and ˆθ2 given by θ. Which estimate is the best when θ = 0.2? 1X2X3(X1+ X2 + X3),10(X1 +345

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Answered: a group of people are having a charity…

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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a group of people are having a charity fair by having a lottery. Every participant can win in three idependent rounds. The chance og winning in every round are different. the probability to win in round 1 is θ, round 2: 4θ, and round 3: 5θ. θ <max(1/4, 1/5). in round 2 and three does every participant have the chance to win regardless of prevoius wins. X_1,X_2,and X₃determine if you win. X_j= 1 if you win, if not 0.

You want to estimte the probabililty θ from the three observations. X1, X2 and X3 with the following estiamtions (picture)
Show that both estimates are right of expectation. Find an expression for the variance to ˆθ1 and ˆθ2 given by θ. Which estimate is the best when θ = 0.2?