Consider the population described by the probability distribution shown below. T

Question

Consider the population described by the probability distribution shown below. The random variable is observed twice x P(x) l Sample |3,3 34 3,5 3,6 43 44 4,5 46 Full data set Question Help 3 02Probability O.04 0.06 0.08 0.02 0,06 0.09 0.12 0.03 4 0.3 5 0.4Sample 5,3 5,4 5,5 5,6 6,3 6,4 6,5 6,6 a. Complete the sampling distribution table. Type the x values in ascending order. 3.5 Probablity 004028 (Type exact answers in simplified form.) 5.5 6 022 Enter your answer in the edit fields and then click Check Answer. 4 taining to search PriSc Insert Deete F10 Backspa

Explanation / Answer

From the given table, find the mean of each sample of size 2. For each unique sample mean, add all the corresponding probabilities. The final table is given above.

For example, Mean of 3,3 = (3+3)/2 = 3, There is only one sample with this mean and therefore the probability is 0.04. Do the same for the remaining samples.

X_bar 3 3.5 4 4.5 5 5.5 6 Probability 0.04 0.12 0.25 0.28 0.22 0.08 0.01

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