 Hello and welcome to the session. In this session we will discuss a question which says that find the most likely score in mathematics corresponding to the score of 9 in statistics from the following data. And this data is given to us in which the average score in mathematics is given as 6 and the corresponding standard deviation is 2 root 2 and the average score in statistics is 8 and the corresponding standard deviation is 2 and the correlation coefficient between x and y is equal to 0.919. Now before starting the solution of this question we should know some results. First is the regression coefficient of x and y that is dxy is equal to r into sigma x over sigma y where the coefficient is the standard deviation of x and sigma y is the standard deviation of y. And secondly the regression equation on y is given as x bar is equal to dxy into y minus y bar the whole. Where x is the mean value of x, y bar is the mean value of y and dxy is the regression coefficient of x and y. Now these results will work out as a key idea for solving out this question. And now we will start with the solution. Now in the equation the data is given to us and according to this the average score in mathematics is 6 that is the mean value of x is 6, the mean value of y is y and is equal to 0.919. So given the mean value of x that is x bar is equal to 6, the mean value of y that is y bar is equal to the standard deviation of x that is sigma x is equal to 2 root 2 that is r is equal to 0.919. Now using this result which is given in the key idea the regression point that is dxy is equal to r into sigma x over sigma y which is equal to which is 0.919 into sigma x which is 2 root 2 this is equal to now we have to find the most likely score in mathematics that is coming to the score of 9 is the value of x when y is equal to we know that the line gives the best estimated value of x or given value of y which is given in the key idea equation of x and y to estimate the value the regression equation is equal to dxy into y minus y bar the whole. Now x bar is 6, y bar dxy is equal to 1.30 these values here this implies is equal to 1.30 into y bar y is equal to 1.1 now to estimate the value of x we will put y is equal to 9 equation number 1 and then we have 0.30 for 0.4 and 7 minus 4.4 of 9 which is not the given equation and that's all for this session hope you all have enjoyed the session.