18. Let Z(t) = X(t)- aX(t-s) where X(t) is the Wiener process. (a) Find the pdf of y(t). (b) Find mean and autocovariance functions.
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- 3. Find f. (g) f'(x) = 2x – e" A A A A A A A search F2 F3 F4 F5 F6 F7 F8 F9 F10 F11 23Let f(x) = | cos t dt ,x> 0. Then f(.x) has %3D (a) maxima when n = - 2, - 4, - 6, . . .. (b) minima when n = 0, 2, 4, | ... . .... (c) minima when n = 1, 3, 5, .... (d) None of thesee joint pdf for X1 and X2 isf (x1, x2) = x1x236for x1 = 1, 2, 3 and x2 = 1, 2, 3.(a) Find the pdf of Y = X1X2.(b) Find the pdf of Z = X1X
- a red coin as a 1 on one side and a 3 on the other. a blue coin has a 0 and 1. let X represent the total of both coins ,Y= number flipped on the blue coin. find(x,y) draw the pdf find fx(X) and fy(Y)Find the first partial derivatives of the function. R(p, q) = tan (pq*) R,(p, q) R,(P, q)Analyze the stationary points of f(x) = x2ex by applying the second-orderderivative test.
- Suppose X and Y are the coordinates of a randomly sampled point in the triangle with vertices (- O), (0,1). (This means their joint PDF is a constant). Find the joint PDF of X and Y, call if f (x,y). Find fy (y)find δƒ/δx and δƒ/δy. ƒ(x, y) = (x + y)/(xy - 1)find δƒ/δx and δƒ/δy. ƒ(x, y) = x/ (x2 + y2)
- Find the linearization L(x) at x=a. Define h(x) = dt a) Evaluate h(x) for x = 2, 4, 6, 8, 10. Plot the five points on h(x) which are determined by these five values of x. b) Display plots of h(x) and In(x) in the same window for 1< x< 11. c) Repeat part (b) for h(x) and k(x) = 0.1 + In(x). d) You should notice that h(x) behaves like a logarithm function, although it has been defined as an integral.Let r(x) = f(g(x)) and s(x) = g(f(x)), where f and g are shown in the figure. Find r'(1) and s'(4). y (6, 6) 5 (6, 5) 4 (2, 4) f 2 1 4 6. (a) r'(1) = (b) s'(4) = Need Help? Read It 3. 2, 6.