
p x + y+ 2z Subject to x+ 2y + 2z 60 2x +y + 3z 60 +3y+ 6z s 60 Maximize x, y,z 2 0
p x + y+ 2z Subject to x+ 2y + 2z 60 2x +y + 3z 60 +3y+ 6z s 60 Maximize x, y,z 2 0
The accompanying tree diagram represents a two-stage experiment. (Let x = 0.3, y = 0.7, r = 0.6, s = 0.4, t = 0.5, and w = 0.5.) Label all branches of the tree diagram and final outcomes. (Note: final outcomes are the results of the Product Rule). Use the diagram to find the following. Provide exact results: 1. ?(?) 2. ?(? ? ) 3. ?(?| ?) 4. ?(?| ?) 5. ?(? ? ∪ ?) 6. ?(? ∪ ?)
emergency
p er ove graphically using branch and bound. Show your graphical solutions on the rap below and show the final branch and bound tree. Max 2x + y St. x + y 3 5 yos -X + ys 0 0 - 0 6x + 2y=21 x 3.5 = 10.5 x20, 20, x,y integer * LO * | 4 | 2% + 2,5 2,5 715 000 may -6x+2y = 21 (215, 2.5 27.5 on solo X 22 L-2 (213 757...
Suppose X, Y are independent and X~N(1,4) and Y N(1,9). If P(2X Y a) P(4X - 2Y 2 4a), then find a
a - e
(a) X + y +z = 11 X – Y – 2= -3 -2 + y - 2 = 5 (3x – y + 2z = 2 (b) x+y+z+t+p=17 X - Y - 2-t-p= -5 z +t+ p + y = 11 p - x - y = 1 -t + x = 10 (c) x +y + 2+t= -6 X - Y - 2 -t = 20 y - X=-39 2x + 3t + y -...
- 2 (3) (a) (7 points) Let w = I = + +7, y = cos(2), z = 4t. Use the Chain Rule to express or in terms of t. Then evaluate du at t= . (b) (7 points) Let w = 2+2y-42 es cos(3t), y e28sin(3t) and 2 = = 22 2r-y+3z) Use the Chain Rule to express and in terms of s and t. = 2 = ow os 8 åt
using the general power rule
Question 1 let y = (x2 +x)3 Find y' 2x+1 3(x2+x)2 3(x2+x)2 (2x+1) • (x2+x)2 (2x+1) recall general power rule formula has three parts: [u(x)" ]' = n u(x)" 1 u'(x) Question 2 let y = (x3 +x2) 1/3 Find y' (x3 +x2) 1/3 (1/3) (x3 +x2) 1/3 . (1/3)(x3 +x2)-2/3 (1/3)(x3 +x2-2/3 (3x2+2x) recall general power rule has three parts. [u(x)"l' = n u(x)n-1 u'(x) Question 5 let g(x) = 1/(x3+x2)3 find g'(x) (x²+x23...
3. (20 p.) Let 2x-2y + 6z = 18 , 3y =-6x + 15 and -9z + x +2y-7-0. Solve this linear equation system for variable y by using Cramer rule.
X and Y are random variables (a) Show that E(X)=E(B(X|Y)). (b) If P((X x, Y ) P((X x})P({Y y)) then show that E(XY) = E(X)E(Y), i.e. if two random variables are independent, then show that they are uncorrelated. Is the reverse true? Prove or disprove (c) The moment generating function of a random variable Z is defined as ΨΖφ : Eez) Now if X and Y are independent random variables then show that Also, if ΨΧ(t)-(λ- (d) Show the conditional...
Let X ~ N(0,1), and let Y = 2X + 5. Compute P(Y <= 7)?