Question

Please show all steps! I need help showing  $Y_{1}-Y_{2}\sim N(0,2\sigma ^{2})$. How do you do the mgf

Answer 1

Question - YNN/4,62) ; M.GIF = My, lt)s élt='72 Y ~ N(4,62) ; M.G.F. Myz(t) = et + 2 t + 1 / 2 242 M.6.F. of (4-Y) - My, Y2 (+)= My, 17). M_yz(+) = My, (+). Mysl-t) Mt+1/2 6242 17+ / 6242 e My-(+) = ež. (202)12 Thus Y, Y₂ ~ N10,262) / Auswer 2 vie. Y-Y2 202 N/0,1) ie Y, Y2 12oz (41-4₂) 2x lie. ie. a) ~x? 202

2 var 02 se var (22) = 20 . re ot Meure Ele) = 1 and ) E(82²) = 0² and Var (82) = 2 MSE C)- Vasco) 204 sunce, YiYz, ---, Yo credo N(4,64) Then 2 Yi-Y (n-1)3² ~xime je (n-1)0,2 wa ie (n-1) Hence ie E (02) 52 E [(nu) 6 )= (1-1) war . (open)-260) and le var (12)= 2(M) re. Vas (62) = 204 (n-1)

Thus, MSECO) وی 2 2 Efficiency Var(82) = (ny) 2 relative to a MSE (82) MS EC) of - E 204 (n-1) 28 Auswer