Consider the population described by the probability distribution shown in the t

Question

Consider the population described by the probability distribution shown in the table. The random variable x is observed twice. If these observations are independent, all the different samples of size 2 and their probabilities are shown in the accompanying table. Complete parts a through c below Click the icon to view the table More Info a. Show that x is an unbiased estimator of . Find and E (x) P(x) 0.2 0.3 0.2 0.2 Type integers or decimals.) 1.0 1.5 2.0 2.5 3 3.5 44.5 5 P(x)0.04 0.12 0.17 0.16 0.18 0.16 0.09 0.04 0.04 Full data set Probability 0.02 0.04 0.02 0.03 0.02 0.01 0.02 0.04 0.06 0.04 0.02 0.04 Sample Mean Probability Sample Mean 0.04 0.06 0.04 0.02 0.04 0.06 0.09 0.06 0.03 0.06 0.04 0.06 3,4 3,5 3.5 4.0 2.5 3.0 3.5 4.0 4.5 3.0 3.5 4.0 4.5 5.0 2.0 2.5 3.0 1,3 1,5 4,3 2.0 2.5 3.0 3.5 2.0 2.5 4,5 5,1 5,2 5,3 5,4 5,5 2,3 2,4 2,5 nter your answer in the edit fields and then click Check Ans parts 3,2

Explanation / Answer

a) = E(X) = 1 * 0.2 + 2 * 0.3 + 3 * 0.2 + 4 * 0.1 + 5 * 0.2 = 2.8

E(X bar) = 1 * 0.04 + 1.5 * 0.12 + 2 * 0.17 + 2.5 * 0.16 + 3 * 0.18 + 3.5 * 0.16 + 4 * 0.09 + 4.5 * 0.04 + 5 * 0.04 = 2.8

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