##### 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