Concepts of Statistics - Bivariate Frequency Distribution

The following table gives the ages of husbands and wives 

Find : (i) The marginal frequency distribution of the age of husbands.
(ii) The conditional frequency distribution of the age of husbands when the age of wives lies between
25 - 35.

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

`"X - 5"/7` and  `"Y - 3"/8`

A bakerman sells 5 types of cakes. Profits due to the sale of each type of cake is respectively Rs. 3, Rs. 2.5, Rs. 2, Rs. 1.5, Rs. 1. The demands for these cakes are 10%, 5%, 25%, 45% and 15% respectively. What is the expected profit per cake?

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.

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)

If for a bivariate data `barx = 10,  bary = 12, V(X) = 9, σ_y = 4` and r = 0.6, estimate y  when x = 5.

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.