Need help with this wronskian problem y1(x)=e^(x) * cosx & y2(x)=e^(x) * sinx Find the values of the wronskian y1,y2 Determine if the solutions are linearly independent
3. (30pt) Suppose that E(Y) = 1, E(Y2) = 2, E(Y3) = 3, V(Y1) = 6, V(Y2) = 7,V (Y3) = 8, Cov(Yı, Y2) = 0, Cov(Yı, Y3) = -4 and 10 1 2 3 Cov(Y2, Y3) = 5. Also define a = 20 and A = 4 5 6 30/ ( 7 8 9 (a) (10pt) Find the expected value and variance covariance matrix of Y, where Y = Y2 (b) (10pt) Compute Eſa'Y) and E(AY). (c) (10pt) Compute...
2. [x] Suppose that Y1, Y2, Y3 denote a random sample from an exponential distribution whose pdf and cdf are given by f(y) = (1/0)e¬y/® and F(y) =1 – e-y/0, 0 > 0. It is also known that E[Y;] = 0. ', y > 0, respectively, with some unknown (a) Let X = min{Y1,Y2, Y3}. Show that X has pdf given by f(æ) = (3/0)e-3y/º. Start by thinking about 1- F(x) = Pr(min{Y1,Y2, Y3} > x) = Pr(Y1 > x,...
15. (30 points) Let Y1 < Y2 < Y3 < Y4 be the order statistics of a random sample of size n = 4 from a distribution with p.d.f.f(x) 2x, 0 < x < 1, zero elsewhere. Evaluate E[Yalyj]. [Hint: First find the joint p.d.f. of Y3 and Y4, and then find the conditional p.d.f. of Y4 given Y3 y3] 15. (30 points) Let Y1
Let Y1, Y2, Y3 be the observation of X. X and Y1,Y2,Y3 are all zero mean real-valued random variables. We are to design a linear estimator. SOLUTION IS PROVIDED ON THE BOTTOM. DON'T NEED TO SOLVE THE PROBLEM MY ONLY QUESTION IS: In part C, c = E[X] Please explain why the inside cancels out and c becomes just E[X] ^This part
3 Question 25 Given a set of DE solutions: y1(x) = e* cos x and y2(x) = e sinx, a) Find the value of the Wronskian W[ v1.y2). b) Determine if the solutions Y1, Y2 are linearly independent. a)W=e b) Linearly Independent a) W=-ex b) Linearly Independent O a) W = 1 b) Linearly Independent a) W=eX b) Linearly Dependent O a) W=0 b) Linearly Dependent None of them
Given y1, y2, and y3 as a function of x. In the same graph plot the three functions for x ?[-3,3] . Follow the form given below. function y1 Line style: solid, color: blue function y2 Line style: dashed, color: black function y3 Line style: dotted, color: red Label the x and y axis; x axis as (x), and the y axis as (y1,y2,y3), title the graph as (problem5), add a legend on the plot. y1=x^4-e^(-x) y2=x^2-x^3+25 y3=30-12x,
Please help on these HW problems It can be shown that yı = x-2, y2 = x-6 and y3 = 7 are solutions to the differential equation xạy" + 11xy" + 21y' = 0. W(y1, y2, y3) = For an IVP with initial conditions at x = 3, C1yı + C2y2 + c3y3 is the general solution for x on what interval? It can be shown that yı = x-2, y2 = x-7 and y3 = 5 are solutions to...
17. Another way to check if y1, y2 are linearly INDEPENDENT in an interval I is: for all I for all I does not exist for all I d. none of the above 18. If y1 is a solution of the equation y "+ P (x) y '+ Q (x) y = 0, a second solution would be y2 (x) = u (x) y1 (x) where u (x) it is: d. all of the above 19. The following set...
Q 3. The joint density of Yı, Y2 is given by e-4342 p(y1, y2) = - T, Y1 = 0,1, 2, ...; Y2 = 0, 1, 2, ... a. Find the marginal distribution of Yı. b. Find the conditional distribution of Y2 given that Y1 = yı. c. Determine if Yı and Y2 are independent - justify; you can use your result from b.