Concepts of Statistics - Bivariate Frequency Distribution

The regression equation of Y on X is y = `2/9` x and the regression equation of X on Y is `x=y/2+7/6` 

Find:

1.  The correlation coefficient between X and Y. 
2.  `σ_y^2 if σ _x^2=4`

Following data gives Sales (in Lakh Rs.) and Advertisement Expenditure (in Thousand Rs.) of 20 firms.
(115, 61) (120, 60) (128, 61) (121, 63) (137, 62) (139, 62) (143, 63) (117, 65) (126, 64) (141, 65) (140, 65) (153, 64) (129, 67) (130, 66) (150, 67) (148, 66) (130, 69) (138, 68) (155, 69) (172, 68)
Construct a bivariate frequency distribution table for the above data by taking classes 115 – 125, 125 –135, ....etc. for sales and 60 – 62, 62 – 64, ...etc. for advertisement expenditure.

Given that X~ B(n = 10, p), if E(X) = 8. find the value of p.

For the bivariate data r = 0.3, cov(X, Y) = 18, σ_x = 3, find σ_y .

Two dice are thrown simultaneously 25 times. The following price of observation are obtained.
(2, 3) (2, 5) (5, 5) (4, 5) (6, 4) (3, 2) (5, 2) (4, 1) (2, 5) (6, 1) (3, 1) (3, 3) (4, 3) (4, 5) (2, 5) (3, 4) (2, 5) (3, 4) (2, 5) (4, 3) (5, 2) (4, 5) (4, 3) (2, 3) (4, 1)
Prepare a bivariate frequency distribution table for the above data. Also, obtain the marginal distributions.

Following data gives the age of husbands (X) and age of wives (Y) in years. Construct a bivariate frequency distribution table and find the marginal distributions.

Find conditional frequency distribution of age of husbands when the age of wife is 23 years.

If the correlation coefficient between X and Y is 0.8, what is the correlation coefficient between:

`"X"/2` and Y

In a bivariate data, n = 10, `bar x` = 25, `bary` = 30 and `sum xy` = 7900. Find cov(X,Y)