Ans.7. Mean_2X-3Y = 2×-2 - 3×1= -7 .
Variance _2X-3Y= 2×4+3×6= 26.
Therefore 2X-3Y normally distributed with (-7,26).
Ans.8. most likely value of X is E(X)= np= 100×.5= 50.
7. If X ~ N(-2,4), Y ~ N(1,6), X.Y are independent, then 2x - 3Y (...
#5. Random variables X and Y have joint PDF 6exp[-(2x+3y)] ,x20, y 20 0 , otherwise x20,y20 (a) Find P[X>Y] and P[X +Y s 1 (b) Find P[ min(x.Y)1] (o) Find P| max(x.y)s1 #5. Random variables X and Y have joint PDF 6exp[-(2x+3y)] ,x20, y 20 0 , otherwise x20,y20 (a) Find P[X>Y] and P[X +Y s 1 (b) Find P[ min(x.Y)1] (o) Find P| max(x.y)s1
Suppose XX and YY are independent random variables for which Var(X)=7Var(X)=7 and Var(Y)=7.Var(Y)=7. (a) Find Var(X−Y+1).Var(X−Y+1). (b) Find Var(2X−3Y)Var(2X−3Y) (c) Let W=2X−3Y.W=2X−3Y. Find the standard deviaton of W.W.
Let X N(1,3) and Y~ N(2,4), where X and Y are independent 1. P(X <4)-? P(Y < 1) =? 4、 5, P(Y < 6) =? 7, P(X + Y < 4) =?
3) Suppose X~N(0,1) and Y~N(2,4), they are independent, then is incorrect. 6 X-Y N(-2,5) D Var(X) < Var(Y) SupposeX-N(Aof) and Y-N(H2,σ ), they arc indcpcndcnt, thcn in the following statementss incorrect 4) 5) Suppose X~NCHiof) and Y~NCHz,σ ), they are independent, if PCIX-Hik 1) > PCIY _ μ2I 1), then ( ) is correct.
3. Suppose x,y,z satisfy the competing species equations <(6 - 2x – 3y - 2) y(7 - 2x - 3y - 22) z(5 - 2x - y -22) (a) (6 points) Find the critical point (0,Ye, ze) where ye, we >0, and sketch the nullclines and direction arrows in the yz-plane. (b) (6 points) Determine if (0, yc, ze) is stable. (c) (8 points) Determine if the critical point (2,0,0) is stable, where I > 0.
Consider an electric field E= 2x i^ - 3y j^ . The coordinates x and y are measured in meters and the electric field is in N/C. What is the magnitude of the flux of this field through a square whose corners are located at (x, y ,z) = (0, 2, 0), (2, 2, 0),(2, 2, 2),(0, 2, 2)? A) 24 Nm2/C B) 6 Nm2/C C) 48 Nm2/C D) 12 Nm2/C E) 0
Let L: R3 → R3 be defined by L(x,y,z) = (2x + 3y – 22,5y + 4z, X – 2). Then, What is the characteristic polynomial p() of L? a) 13 – 622 + 51 – 12 b) 23 – 322 – 42 + 12 c) 13 + 312 – 52 - 12 d) 13 – 622 +52 + 12
B (2,4) A (-2,3) C (11,2) 0 3y+ 2x+5-0 In the diagram, the points A, Band C have coordinates (-2,3), (2,4) and (11,2) respectively. D is a point such that DA is perpendicular to AB, and Dlies on the line 3y+ 2x+ 5 = 0. 141 Find the coordinates of D. Point E lies on DC and the ratio of the length of DE to the length of DCis 2:3 (i) 141 (ii) Find the area of triangle DBE. (ii)...
3. Suppose x, y, z satisfy the competing species equations 2(6 - 2x - 3y - 2) y(7 - 2.0 - 3y - 22) z(5 – 2x - y -22) (a) (6 points) Find the critical point (0, yc, ze) where yc, ze >0, and sketch the nullclines and direction arrows in the yz-plane. (b) (6 points) Determine if (0, yc, ze) is stable. (c) (8 points) Determine if the critical point (1,0,0) is stable, where 8c > 0.
3. Suppose x, y, z satisfy the competing species equations 2(6 - 2x - 3y - 2) y(7 - 2.0 - 3y - 22) z(5 – 2x - y -22) (a) (6 points) Find the critical point (0, yc, ze) where yc, ze >0, and sketch the nullclines and direction arrows in the yz-plane. (b) (6 points) Determine if (0, yc, ze) is stable. (c) (8 points) Determine if the critical point (1,0,0) is stable, where 8c > 0.