Statistics (Entrance Exam) - Bivariate Frequency Distribution

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

${\displaystyle \frac{\text{X - 5}}{7}}$ and  ${\displaystyle \frac{\text{Y - 3}}{8}}$

In a bivariate data, n = 10, ${\displaystyle \overline{x}}$ = 25, ${\displaystyle \overline{y}}$ = 30 and ${\displaystyle \sum xy}$ = 7900. Find cov(X,Y)

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

The price P for demand D is given as P = 183 + 120D - 3D². Find d for which the price is increasing.

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.

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 tale gives income (X) and expenditure (Y) of 25 families:

Find How many families have their income Rs. 300 and more and expenses Rs. 400 and less?

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

${\displaystyle \frac{\text{X}}{2}}$ and Y