 Hello and welcome to the session. In this session we will discuss a question which says that the table shows the number of books sold at a library sale make a table of joint and marginal related frequencies. Now let us start with the solution of the given question. Now in this table that is in this two way table we are given two categories one of fiction and one fiction and other of type of color of books and here the frequencies are 28, 52, 94 and 36. Now to find joint related frequencies we will divide each frequency by the grand total of all frequencies and here this grand total is equal to 28 plus 52 plus 94 plus 36 which is equal to 210. Now here we will make a joint related frequency two way table for this let us calculate joint related frequencies. Now corresponding to heart color in the first cell we will have 28 upon total of all frequencies that is 210 which is equal to 0.13. Then in the next cell we have 52 upon 210 which is equal to 0.25 then corresponding to paper color. In the first cell we have 94 upon 210 which is equal to 0.45 and in the next cell we have 36 upon 210 which is equal to 0.17. So this is the required joint related frequency two way table. Now to find marginal related frequency table we add the joint related frequency of each column and row. Now for row one the marginal related frequency is 0.13 plus 0.25 which is equal to 0.38 and for row two the marginal related frequency is 0.45 plus 0.17 which is equal to 0.62. And for column one the marginal related frequency is 0.13 plus 0.45 which is equal to 0.58 and for column two the marginal related frequency is 0.25 plus 0.17 which is equal to 0.42 and this is the table of joint and marginal related frequencies. Now let us check our calculations. Now the total of marginal related frequencies of row should be 1 and total of marginal related frequencies of column should also be 1. Now here we can see total of marginal related frequencies of rows is 0.38 plus 0.62 which is equal to 1 and total of marginal related frequencies of columns is 0.58 plus 0.42 which is again 1. Hence total of marginal related frequencies of rows is equal to total of marginal related frequencies of columns which is equal to 1. And this is the solution of the given question. That's all for this session. Hope you all have enjoyed the session.