I have been presented with the following question:
"On your shelf you have four books that you are planning to read in the near future. Two are fictional works, containing 212 and 379 pages, respectively, and the other two are nonfiction, with 350 and 575 pages, respectively.
(c) Suppose that you randomly select one of the two fiction books and independently randomly select one of the two nonfiction books. Obtain the sampling distribution of X for this sampling method, and determine its mean and standard deviation."
For this question i am having trouble setting up the sampling distribution. Does "independently randomly select" indicate that i am sampling WITH replacement? This doesn't seem to make sense considering i can't choose two of the same books..My thoughts were to construct a sampling distribution as such:
Fiction: 212 pages
Fiction: 379 pages
Non-Fic: 350 pages
Non-Fic: 575 pages
x1: 212, 212, 379, 379, 350, 350, 575, 575
x2: 350, 575, 350, 575, 212, 379, 212, 379
X=x: 281, 393.5, 364.5, 477, 281, 364.5, 393.5, 477
xbar: 281, 364.5, 393.5, 477
P(Xbar=xbar): 2/8, 2/8, 2/8, 2/8
My thinking here was that there are 2 fiction and 2 non fiction books; I am to select one fiction and one non-fiction. If i select the first fiction (212 pages) then i can select from either of the 2 non-fiction books. If i select the second fiction (379 pages) then i can select from either of the 2 non-fiction books again. Same principle if i pick one of the Non-Fiction books first.
Am i missing some essential point here? Any hints would be greatly appreciated!