Random variables X and Y have the following joint probabilities: P(X=0,Y=0)=P(X=0,Y=8)=P(X=16,Y=0)=P(X=16,Y=16)=14 a)Make a table of the joint distribution of X and Y and add their marginal distributions to the table. b)Compute Cov(X, Y). Are X and Y positively correlated, negative correlated,or uncorrelated? c)Compute the correlation coefficient between X and Y.

Question

Random variables X and Y have the following joint probabilities: P(X=0,Y=0)=P(X=0,Y=8)=P(X=16,Y=0)=P(X=16,Y=16)=14   a)Make a table of the joint distribution of X and Y and add their marginal distributions to the table.   b)Compute Cov(X, Y). Are X and Y positively correlated, negative correlated,or uncorrelated?   c)Compute the correlation coefficient between X and Y.

Opeance1951 · Accepted Answer

Step 1  The random variables having joint probabilities are given as,   P(X=0,Y=0)=P(X=0,Y=8)=P(X=16,Y=0)=P(X=16,Y=16)=14  a. The joint distribution of X and Y is given as,  X|Y0816Fx(X)01414012161401412Fy(Y)1214141  Step 2  b. The marginal distribution of X is given as,  X016P(x=X)1212  E(X)=∑xxP(X=x)  =0×12+16×12  =8.  E(X2)=∑xx2P(X=x)  =0×12+162×12  =128.  Step 3  The variance of the probability distribution is,  Var(X)=E(X2)−[E(X)]2  =128−64  =64.  The marginal distribution of Y is given as,  Y0816P(y=Y)121414  E(Y)=ExyP(Y=y)  =0×12+8×14+16×14  =2+4.  =6.  Step 4  The value of E(Y2) is,  E(Y2)=∑xy2P(Y=y)  =0  =02×12+82×14+162×14  =16+64.  =80.  The variance of probability distribution is,

Random variables X and Y have the following joint probabilities: P(

Answered question

Answer & Explanation

New Questions in High school statistics