Assume that the set of random variables Y[i] are independent for i = 1.10 (which are approximated by a Gaussian(0,1) distribution). define Z = (sum...

Assume that the set of random variables Y[i] are independent for i = 1..10 (which are approximated by a Gaussian(0,1) distribution). define Z = (sum from i = 1 to 10) Y[i]^2. Show using the properties of moments that E(Y[i]^2) = 1.Note that the square brackets [] are for subscripts, so y[i] is y sub-i. Also note that E() represents the expecation, or expected value.

Since Yi’s are Gaussian (0,1) , we can write Yi ~~ N (0,1)Now we know from the properties of moments thatE (Yi 2 ) = V (Yi ) + E (Yi ) 2Since V (Yi ) = 1E (Yi ) = 0⇒ E (Yi 2 ) = 1