Let the correlation coefficient between X and Y be 0.6. Random variables Z and W are defined as Z = X + 5 and W = $${Y \over 3}$$. What is the correlation coefficient between Z and W ?

If all the natural numbers between 1 and 20 are multiplied by 3, then what is the variance on the resulting series?

The mean of 100 observations is 50 and the standard deviation is 10. If 5 is subtracted from each observation and then it is divided by 4, then what will be the new mean and the new standard deviation respectively?

Let x - 3y + 4 = 0 and 2x - 7y + 8 = 0 be two lines of regression computed from some bivariate data. If b_yx and b_xy are regression coefficients of lines of regression of y on x and x on y respectively, then what is the value of b_xy + 7b_yx?