 Hello and welcome to the session. In this session, we shall discuss the following question and the question says that if a coin is tossed three times and random variable capital X is defined as the number of heads that result from this experiment, draw a table for its probability distribution. Also display it graphically. Now let us start with the solution of the given question. In this question, it is given that a coin is tossed three times so sample space S will be equal to the set containing h, h, h, h, h, h, h, h, t, h, t, h, h, t, t, t, t, t, h, t, t, t, t, t, t, where h denotes H denotes the occurrence of head and T denotes the occurrence of tail, so here HHH denotes occurrence of three heads, HHT denotes occurrence of two heads followed by a tail and so on. Here total number of outcomes are given by 8. Here capital X is defined as the number of heads that result from this experiment. Now we find small x by assigning numerical value to each sample point. Now see the sample space here for HHH we assign the value of small x as 3. Now for HHT, HTH and THH we assign the value of small x as 2 for HTT, THT and TTH we assign the value of x as 1 and for TTT we assign the value of x as 0. Now the small x indicates the number of heads that result from this experiment and here we have the number of heads as 0. Here the number of heads are 1, here the number of heads are 2 and here the number of heads are 3. Now let us draw a table for probability distribution. Now here in column 1 we have written all the small x values and in column 2 we will write the probability values that is we will write the probability of capital X is equal to small x. So here when the value of small x is equal to 3 probability of capital X is equal to 3 will be given by number of favourable outcomes that is equal to 1 upon total number of outcomes that is equal to 8. Here we see that the number of favourable outcomes to this event is 1. Similarly probability of capital X is equal to 2 is equal to 3 upon 8. The probability of capital X is equal to 1 is equal to 3 upon 8 and the probability of capital X is equal to 0 is equal to 1 upon 8. Now here 1 upon 8 is equal to 0.125, 3 upon 8 can be written as 0.375, 3 upon 8 can be written as 0.375 and 1 upon 8 can be written as 0.125. Now we display it graphically. Now here is the graph for probability distribution where we have taken the small x values along horizontal axis and probability values along vertical axis. The probability of capital X is equal to 0 is shown as 0.125. The probability of capital X is equal to 1 is shown as 0.375. Similarly the probability of capital X is equal to 2 is shown as 0.375 and the probability of capital X is equal to 3 is shown as 0.125. Which implies that when number of heads is equal to 0 then the probability is 0.125, when number of heads is equal to 1 then the probability is 0.375, when number of heads is equal to 2 then the probability is 0.375 and when the number of heads is equal to 3 then the probability is 0.125. Hence we get the required probability distribution graph. This completes our session. Hope you enjoyed this session.