Roll a fair 4-sided dice twice. If A=first roll and B=second roll, then let X=the min(A,B) and Y = |A-B|. a) Give the joint distribution b) Find Cov(X,Y) Solution a) Joint Distribution: (A,B)---->(X,Y) (1,1)---->(1 ,0) (1,2)---->(1,1) (1,3)---->(1,2) (1,4)---->(1,3) (2,1)---->(1,1) (2,2)---->(2,0) (2,3)---->(2,1) (2,4)---->(2,2) (3,1)---->(1,2) (3,2)---->(2,1) (3,3)---->(3,0) (3,4)---->(3,1) (4,1)---->(1,3) (4,2)---->(2,2) (4,3)---->(3,1) (4,4)---->(4,0) b) Cov (X,Y)= E(XY) -E(X)E(Y) E(X) = 30 /16 ( Summation X =30) E(Y) = 20/16 (Summation Y=20) E(XY) = 30/16 (Summation XY =30) Therefore, Cov (X,Y) = 30/16 - ( 30/16 * 20/16) = - 0.4687 ( Negative Correlation ) Answer.

1. Select all the functions below that are the primary responsibilities of the endocrine system.
Regulates water and electrolyte balance Breaks down nutrients Causes movement of muscles
Delivers oxygen Regulates metabolism Controls reproduction and development Provides
structure Removes wastes Regulates growth
Solution
Regulates water and electrolyte balance
Breaks down nutrients( for absorption)
Regulate metabolism
Regulates growth
Controls of reproduction and development
The above are the primary functions of endocrine system.