X p(x) X P(x) 1 0.1 1,1 1,2 1,3 1,4 1,5 2,1 2,2 2,3 2,4 2,5...

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X p(x) X P(x) 1 0.1 1,1 1,2 1,3 1,4 1,5 2,1 2,2 2,3 2,4 2,5 3,1 3,2 3,3 Sample Mean 1.0 1.5 2.0 2.5 3.0 1.5 2.0 2.5 3.0 3.5 2.0 50 1.0 1.5 2.0 2.5 3 3.5 0.01 0.08 0.2 0.18 0.16 2.5 2 0.4 3.0 3 0.2 Probability Sample 3,4 3,5 0.01 0.04 0.02 0.01 0.02 0.04 0.16 0.08 0.04 0.08 0.02 0.08 0.04 4 0.1 4,1 4,2 4,3 4,4 4,5 5,1 5,2 5,3 5,4 5,5 5 0.2 Mean 3.5 4.0 2.5 3.0 3.5 4.0 4.5 3.0 3.5 4.0 4.5 5.0 4 4.5 5 0.04 0.2 0.09 0.04 Probability 0.02 0.04 0.01 0.04 0.02 0.01 0.02 0.02 0.08 0.04 0.02 0.04 Full data set 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. a. Show that x is an unbiased estimator of μ. Find μ and E (X). μ= E(X) = (Type integers or decimals.) X p(x) X P(x) 1 0.1 1,1 1,2 1,3 1,4 1,5 2,1 2,2 2,3 2,4 2,5 3,1 3,2 3,3 Sample Mean 1.0 1.5 2.0 2.5 3.0 1.5 2.0 2.5 3.0 3.5 2.0 50 1.0 1.5 2.0 2.5 3 3.5 0.01 0.08 0.2 0.18 0.16 2.5 2 0.4 3.0 3 0.2 Probability Sample 3,4 3,5 0.01 0.04 0.02 0.01 0.02 0.04 0.16 0.08 0.04 0.08 0.02 0.08 0.04 4 0.1 4,1 4,2 4,3 4,4 4,5 5,1 5,2 5,3 5,4 5,5 5 0.2 Mean 3.5 4.0 2.5 3.0 3.5 4.0 4.5 3.0 3.5 4.0 4.5 5.0 4 4.5 5 0.04 0.2 0.09 0.04 Probability 0.02 0.04 0.01 0.04 0.02 0.01 0.02 0.02 0.08 0.04 0.02 0.04 Full data set 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. a. Show that x is an unbiased estimator of μ. Find μ and E (X). μ= E(X) = (Type integers or decimals.)

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