Question

Probability and Statistics for En 202 Lab Manual Summer 20 X olicFiles/School/Textbooks/STAT383 Stats.pdf 5.2.3 Problems 5.2.1 Suppose that X Z N(12.0, 7.5) are independent random variables. Find the probability that (a) XY0 (b) X+Y 2Z-20 N (3.2, 6.5), Y N(-2.1, 3.5), and (c) 3X+5Y >1 (d) 4X 4Y + 2Z< 25 (e) |X +6Y + Z| 2 2 (f) 12X Y6

Answer 1

Elx+ Yコ v [x) VxJ 3.57.5 ニ U Slomclond dev - メ+Y ~ N 2= Xーム P(x+Y0) P (z-1) P (z-o.33 O.629 3 E [x+Y-2z 3.2 2.1- 24 22.g V[xt Y 22 Vx+vY]4Vz] &.5+3.5+4x5 40 P 2 -20+ P (z<0.46) V 4-0 O.6772

5-2.1) -09 ニ 3×3.2 + ET3x+51 9V[x] 25 VlY) vI3x+5Y) 1 O,9 P(z 146 ( 91 0 z)d O.434 E [4x -4 Y +2 Z 4x3.2 + 4x2. 1+ 2x12 45,2 v [4x- 4Yt1z] 16 vTxJt 16V[Y]+4V[z] ニ 16x65ナ6x 3.5 +4x75 19 0 25-45, 2 ラz V190 P (z (tヤリ- > O.0708