 Hello and welcome to the session. In this session we are going to discuss the following question and the question says that the number of television sets which is denoted by capital X in a family chosen at random has following probability distribution find the average number of television sets in the family that is expected value of capital X let us start with the solution of the given question here we are given a table that shows probability distribution for the number of television sets that is capital X we have to find the average number of television sets in the family that is the expected value of capital X we know that if capital X is a random variable with possible values denoted by small x i and probability of small x i that is probability of capital X is equal to small x i denotes its probability distribution then expected value of capital X which is denoted by mu is equal to summation of small x i into probability of small x i where i varies from 1 to n so here we have expected value of capital X will be equal to summation of small x i into probability of small x i where i varies from 1 to n and here we will have expected value of capital X will be equal to summation of small x i into probability of small x i where i varies from 1 to 345 that is 5 and here this is equal to 0 into 0.01 plus 1 into 0.34 plus 2 into 0.19 plus 3 into 0.24 plus 4 into 0.22 and this is equal to 0 into 0.01 is 0 plus 1 into 0.34 is 0.34 plus 2 into 0.19 that is 0.38 plus 3 into 0.24 that is 0.72 plus 4 into 0.22 that is 0.88 and this is equal to 2.32 so expected value of capital X is equal to 2.32 which is approximately equal to 2 thus average number of television sets in our family is 2 approximately which is the required answer this completes our session hope you enjoyed this session