X1,..., X are i.i.d. standard normal variables. Denote by An the sample mean of the squares of these variables: 1.:- x - - * - }(x2 + x3 + .. + x2). 1 Recall An= = x. For very large n, the distribution of (An-a) is approximated best by ... (In the choices below, the parameter for the normal distributions N (4,0") are the mean w and the variance o?.) O N (0,1) O N (0,2) O N (0,n) O N (0,2n) O x x. Define a sequence of random variables B, Does the sequence of random variables Bre n converge in probability to a constant b? If yes, enter the value of b below, if no, enter "DNE". (Enter e for the constant e)
B6- As above, let a be the limit in probability of An, ie. An a, and b be the limit in probabiity of Bn = 4, i.e. Br*b, if these limits exist. Does the sequence of random variables (Br-b) converge in distribution? Choose the correct characterization of the limit distribution: O N (0,1) O N 0, "Var (X2) O N (0, "Var (x2)) O N (0, 24Var (X²)) O N 0, e?Var (An)) O Does not converge in distribution