 Hi and welcome to the session, I am Shashi and I am going to help you with the following question. Question says, in a meeting 70% of the member favour and 30% oppose a certain proposal, a member is selected at random and we take x is equal to 0 if he opposed and x is equal to 1 if he is in favour, find mean of variable x and variance of variable x. Let us now start with the solution. Now we are given, we write random variable x is equal to 1 if member favours a certain proposal. We are also given that we take random variable x is equal to 0 if member opposed a certain proposal. Now we will write the probability distribution of random variable x. You know random variable x can assume two values only that is 0 or 1. Now we are given that 70% of the members favour a certain proposal and 30% of the members oppose a certain proposal. And we also know that we take x is equal to 1 when a member favours a proposal and we write x is equal to 0 when a member opposes a proposal. Now when x is equal to 1, px is equal to 70 upon 100. You know we can write 70% as 70 upon 100 which is further equal to 0.70. Similarly when x is equal to 0, px is equal to 30 upon 100. We know 30% can be written as 30 upon 100 which is further equal to 0.3. Now for x is equal to 0 we have px is equal to 0.3. So here we can write 0.3 and for x is equal to 1 we have px is equal to 0.70. So here we can write 0.70. Now we know mean of random variable x is equal to ex which is given by summation of xi pxi where i is equal to 1 to n. Now mean of random variable x is equal to x1 p1 plus x2 p2. So here we can write 0 multiplied by 0.3 plus 1 multiplied by 0.70. Now we know 0 multiplied by 0.3 is equal to 0 only and 1 multiplied by 0.70 is equal to 0.70. So mean of variable x is equal to 0.70. Now we will find variance of variable x is equal to ex square minus ex whole square. Now first of all we will find out ex square is equal to summation of xi square multiplied by pxi where i is equal to 1 to n. So we get ex square is equal to 0 square multiplied by 0.3 plus 1 square multiplied by 0.70. Now square of 0 is equal to 0 only and 0 multiplied by 0.3 is equal to 0. Now square of 1 is equal to 1 and 1 multiplied by 0.70 is equal to 0.70. So we get ex square is equal to 0.70. Now we will find variance of variable x is equal to 0.70 minus square of 0.70. We know value of ex square is equal to 0.70 and value of ex is equal to 0.70. And we have written this square as it is. Now this is further equal to 0.7 minus 0.49. Now subtracting these two terms we get 0.21. So variance of x is equal to 0.21. So we get mean of variable x is equal to 0.7 and variance of x is equal to 0.21. This is our required answer. This completes our session. Hope you understood the solution. Take care and have a nice day.