 Hello, and welcome to the session. I am Deepika here. Let's discuss a question which sees find me new Variant sigma square for the following probability distribution if x is equal to 0, px is equal to 1 over 8 4x is equal to 1, px is equal to 3 over 8, 4x is equal to 2 3x is equal to 3 over 8 and for x is equal to 3, px is equal to 1 over 8 Now we know that the mean mu is equal to the expectation of x which is equal to sigma xi pi i varying from 1 to n Again variance of x is equal to e x square minus e x Whole square So this is a key idea behind our question We will take the help of this key idea to solve the above question So let's start the solution Now according to our key idea the mean mu is equal to e x Which is given by sigma xi pi i varying from 1 to n So this is equal to 0 into 1 by 8 plus 1 into 3 over 8 plus 2 into 3 over 8 plus 3 into 1 over 8 And this is further equal to 0 Plus 3 over 8 Plus 6 over 8 Plus 3 over 8 And this is again equal to 3 plus 6 plus 3 over 8 which is further equal to 12 over 8 And this is equal to 3 over 2 So the mean of the above probability distribution is 3 over 2 Now for the variance Of x we will first find out e x square which is equal to 0 into 1 over 8 plus 1 square into 3 over 8 Plus 2 square into 3 over 8 plus 3 square into 1 over 8 And this is further equal to 0 plus 1 into 3 over 8 plus 4 into 3 over 8 plus 9 into 1 over 8 And this is again equal to 0 plus 3 over 8 plus 12 over 8 plus 9 over 8 And this is again equal to 3 plus 12 Plus 9 over 8 And this is further equal to 24 over 8 Which is again equal to 3 Now according to our key idea we have Variance of x is equal to e x square minus e x Whole square So this is equal to Now we have e x square is equal to 3 and E x is equal to 3 over 2 So variance of x is equal to 3 minus 3 over 2 Square and this is equal to 3 minus 9 over 4 Which is further equal to 12 minus 9 over 4 And this is equal to 3 over 4 So the answer for the above question is mean of x That is expectation of x Is equal to 3 over 2 and variance of x Is equal to 3 over 4 So this is the answer for the above question This completes our session I hope the solution is clear to you. Bye and have a nice day