Reference no: EM132606778

QUESTION ONE
The following table shows a joint probability mass function f(x,y)

function f(x,y)
 
                      X       
         0             1                  2       
          
     0 1/16      2/16          1/16
 Y  1  2/16     4/16          2/16
     2  1/16     2/16          1/16        
Total  4/16     8/16           4/16    

Find :
P(X=0,Y=1)
P(X<Y)
P(X>Y)
P(X=Y)

QUESTION TWO
Find the marginal probability function for the random variable X in question one above
P(X=0)
P(X=1)
P(X=2)

QUESTION THREE

Calculate the covariance and correlation for X and Y using the information from the joint probability mass function in the table given below
                      Y       
         1             2              3                                                         

 X  1   0           0.1             0         

     2   0.3        0.2            0.1

     3   0            0.3           0         

P(Y)  0.3         0.6          0.1

QUESTION FOUR

The following table shows marks scored by 15 students in Mathematics and English test: Use it to calculate the correlation coefficient

STUDENT    MATHEMATICS (X)    ENGLISH (Y)       
1    84    69       
2    74    64       
3    48    56       
4    54    72       
5    72    86       
6    71    68       
7    96    87       
8    75    86       
9    69    71       
10    100    91       
11    23    31       
12    58    65       
13    94    89       
14    76    71       
15    52    54    

QUESTION FIVE

Find the regression of Y on X in question four (4) above