 Hello and welcome to the session. In this session we will discuss if a specified model is consistent with results from a given data generating process. Now let us take the model of flipping a coin. How do you know if a coin is fair? That is when you flip it, how do you know if a coin is equally likely to land heads or tails. You can flip an actual coin many times to help you decide whether you think it's fair. But sometimes unusual outcomes appear while flipping the coin that we never expect. We become doubtful about fairness of the coin. Let us consider an example. Suppose we flip a coin four times and we get tails in all the four trials. Now would you say that the coin is unfair? What will you do to know whether the coin is fair or unfair? To know this we will try to construct a physical model of flipping a coin. Then we will come to know whether the coin is fair or unfair. So here we conduct an experiment and that is there are ten students in our class and each student is asked to flip a coin four times in ten trials and note the reading in each trial since the coin is tossed four times. So in each trial the following outcomes can be there that is four heads, three heads and one tail, two heads and two tails, one head and three tails or four tails. So these are five possible outcomes each student recorded its ten trials. So number of trials for each student is given as ten. The data of all the ten students was collected and recorded. So total number of trials is equal to hundred because one student performed ten trials. So ten students performed ten into ten that is hundred trials and frequency of each outcome was recorded in the form of a table and the given frequency table is as follows where in all the four trials the outcome of four heads occurred six times, three heads and one tail occurred twenty two times, two heads and two tails occurred forty four times, one head and three tails occurred eighteen times and four tails occurred ten times and if we add all the frequencies over here we get hundred that is the total number of trials. Now we shall draw a biograph for this data. On horizontal axis we take outcomes and on vertical axis we take frequency and here on horizontal axis we have written outcomes that is four heads, three heads and one tail, two heads and two tails, one head and three tails and four tails. Now we write on vertical axis that is we take frequency with a scale of ten so here we have the frequencies zero, ten, twenty, thirty, forty, fifty and sixty. Now from the table we can see that frequency of outcome that is four heads is six so we draw a bar of height six, next frequency of outcome that is three heads and one tail is twenty two so we draw a bar of height twenty two, next we have frequency of outcome two heads and two tails is forty four so we draw a bar of height forty four, frequency of outcome one head and three tails is eighteen so we draw a bar of height eighteen and lastly we have frequency of outcome that is four tails is ten so we draw a bar of height ten so we have this biograph. Now see the highest bar it shows that maximum times two heads and two tails appeared and we can say that two heads and two tails appeared forty four times out of hundred trials so we can say that in flipping a coin four times two heads and two tails appear the maximum number of times which shows equal chance of coming of head and tail so we arrive at the conclusion that the coin is fair so this model shows that with only one trial and coming of four tails in a row we cannot say that coin is unfair this completes our session hope you enjoyed this session