Fundamentals of Mathematical Statistics (BCA) 1st Sem Previous Year Solved Question Paper 2022

To find the values of x and y, as well as the coefficient of correlation, we can use the given regression equations:

1. Regression equation of X on Y: 10x - 2y = 4
2. Regression equation of Y on X: 2y - 5x = 8

We can solve this system of linear equations to find the values of x and y.

Let's first solve for y in terms of x using the equation (1):

10x - 2y = 4

-2y = 4 - 10x

y = (10x - 4) / 2

y = 5x - 2

Now, substitute this expression for y into the equation (2):

2(5x - 2) - 5x = 8

10x - 4 - 5x = 8

5x - 4 = 8

5x = 8 + 4

5x = 12

x = 12 / 5

x = 2.4

Now that we have found the value of x, we can find the value of y using the equation for y:

y = 5x - 2

y = 5 * 2.4 - 2

y = 12 - 2

y = 10

So, the values of x and y are:
x = 2.4
y = 10

Now, to find the coefficient of correlation (r), we can use the relationship between the regression coefficients:

r = ± √(bxy * byx)

Where bxy is the regression coefficient of X on Y and byx is the regression coefficient of Y on X.

From the given equations:
- Regression equation of X on Y: bxy = 10
- Regression equation of Y on X: byx = 5

Now, calculate the coefficient of correlation:

r = ± √(10 * 5) = ± √50 ≈ ± 7.07 (rounded to two decimal places)

So, the coefficient of correlation (r) is approximately ±7.07, indicating a strong positive linear correlation between X and Y. The positive or negative sign depends on the direction of the correlation.