Hello. I need help with part B please. I have answered A already. Consider the f

Question

Hello. I need help with part B please. I have answered A already.

Consider the following population: {20, 21, 22, 23}. Note that the population mean is the following.

Compute the sample mean for each of the 12 possible samples.

Use this information to construct the sampling distribution of x. (Display the sampling distribution as a density histogram.)

Use the histogram to complete the table. (Enter the probabilities as fractions.)

(b) Suppose that a random sample of size 2 is to be selected, but this time sampling will be done with replacement. Using a method similar to that of Part (a), construct the sampling distribution of x. Hint: There are 16 different possible samples in this case. (Enter the probabilities as fractions.)

Use the histogram to complete the table.

20, 21 20, 22 20, 23 21, 20 21, 22 21, 23 22, 20 22, 21 22, 23 23, 20 23, 21 23, 22 20 21 22 23 21.5

Explanation / Answer

from above

adding up the duplicate probabilities below is the final table

please revert for doubt

X1 X2 Sample mean P(x1,x2) 20 20 20 1/16 21 20 20.5 1/16 22 20 21 1/16 23 20 21.5 1/16 20 21 20.5 1/16 21 21 21 1/16 22 21 21.5 1/16 23 21 22 1/16 20 22 21 1/16 21 22 21.5 1/16 22 22 22 1/16 23 22 22.5 1/16 20 23 21.5 1/16 21 23 22 1/16 22 23 22.5 1/16 23 23 23 1/16

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