Let X, Y, and Z be jointly continuous random variables. Assume that all conditional PDFs and expectations are well defined. E. g., when conditioning on X = x, assume that x is such that fX(x) > 0.
For each one of the following formulas, state whether it is true for all choices of the function g or false (i. e., not true for all choices of g ).
1) E[g(Y)|X=x] = ∫ g(y) fY|X(y|x) dy
2) E[g(y)|X=x] = ∫ g(y) fY|X(y|x) dy
3) E[g(Y)] = ∫ E[g(Y)|Z=z] fz(z) dz

Apublic library wants to place 4 magazines and 9 books on each display shelf. the expressions 4s +9s represents the total number of items that will be displayed on s shelves. simplify this expression

Powerful women's group has claimed that men and women differ in attitudes about sexual discrimination. a group of 50 men (group 1) and 40 women (group 2) were asked if they thought sexual discrimination is a problem in the united states. of those sampled, 11 of the men and 19 of the women did believe that sexual discrimination is a problem. if the p-value turns out to be 0.035 (which is not the real value in this data set), then at = 0.05, you should fail to reject h0. at = 0.04, you should reject h0. at = 0.03, you should reject h0. none of these would be a correct statement.

Last month, a 770 g box of cereal was sold at a grocery store for $3.10. however, this month, the cereal manufacturer launched the same cereal in a 640 g box, which is being sold at $2.50. what is the percent change in the unit price?