Manipulations of means and variances.
(a) If E(X) = 1 and V (X) = 5, find E[(2 + X)^2] and V [(2 + X)^2].
(b) If E(X) = 6 and E(X^2) = 50, find E(3X - 4) and V (2X + 4).
Manipulations of means and variances. (a) If E(X) = 1 and V (X) = 5, find...
Two random variables X and Y have means E[X] = 1 and E[Y] = 0, variances 0x2 = 9 and Oy2 = 4, and a correlation coefficient xx =0.6. New random variables are defined by V = -2X + Y W = 2X + 2Y Find the means of V and W Find the variances of V and W defined in question 3 Find Rww for the variables V and W defined in question 3
Problem 5. (2 points) If X,, X, ..X40 are independent random variables with means u, = 2 = ... = H40 = 1, and variances o? = o? = o%o = 1, and if Y = 2X, – 3X, +X3 + X4 + ..+X40 , What are the mean and = ... variance of Y?
Suppose X and Y V(X) = 3 and V(Y ) = 5. Find: (a) V(X + Y ) given that X, Y are independent (b) V(3X + 4) given that X, Y are independent (c) V(X + X) given that E(X · Y ) = −1 (d) V(X + 3Y ) given that E(X · Y ) = 0
E 4 MC Questions 1 - 10 1. 18Ne 19F + 2x +v 2. Ca - Sc + 3x + v 3. Cu -> Cu + 2x 4. Cr -- → + 4x 5. 234 Pu -- 239U + Ax 6. Li + ip -→ He + x 7. 233Np 234Pu + 2x + v 8. 15N + --> H+ x 9. H + H --XX + tie + v 10. He + He -x + 1H + H QUESTION...
Signature: 19.( 9 marks) Find the derivative of the following functions. 1. V = 1 " b. y = sinsx - Cos 3x c. y = (sec 5x + tan-'(1 - x)) 20. (6 marks) Find the derivative of the following functions. a) y = ln(1 - 3x) + 4* b) y = -2x + 3x +1
Use the rules to find the derivative f (x) = -3x e^x^5 + 2cos(2x^2 )
2. Sketch the graph of the following functions and find the values of x for which lim f(x) does not exist. b)/(x) = 1, x = 0 f(x)- 5, x=3 c) x2 x>1 2x, x> 3 d) f(x)-v e) (x)- [2x 1- sin x Discuss the continuity of the functions given in problem #2 above. Also, determine (using the limit concept) if the discontinuities of these functions are removable or nonremovable 3. Find the value of the constant k (using...
x+5 + 4. Solve +7x+2 x-1 212+5x+2 3x28x+4 (a) You know the drill! Factor the denominators! (NOTE: If you need help factoring these polynomials, see Helping Handout: Lab 1B) i. Factor the first denominator: 6x2+7x +2 = ( OC ) ii. Factor the second denominator: 3x+8x+4-( iii. Factor the third denominator: 2x2+5x+2 = ( ) (b) Rewrite with factored denominators: x+5 x-1 X + (2x+ 1)(3x+2) x+2)(3x+2 ) (c) Find the restrictions: (x+2) (2x+1) AND AND (d) Find the LCM:...
32. Simplify : a. x/3-x/4 b. 3/(2x) -4/x c. 1/2x-1/3x 33. Find x if: 3x +6 = 2-5x a. b. x/m + x/n = 1 C 1/x = 3/m d. Sx/3 = 2 34. Find b if: x/(x+a) = 2/b a. b. v(x - b') =y 35. Solve the following Simultaneous linear equations and check in both equations: a) 3x+y=-4 x-2y 1 b) 5x+y=-8 2x-2y 4 Answer: x-1, y.3 36. Evaluate the expression below, if b-3 and c-2. 2bc'+(bc) Helpful...
Solve 5 please 5.7 Exercises In Exercises 1-6 use variation of parameters to find a particular solution. 1. y" +9y = tan 3x 2. y' + 4y = sin 2x sec2 2x 3. y" – 3y' + 2y = 4 4. j" – 2y + 2y = 3e* sec x 1+e-x 4e-x 5. y" – 2y' + y = 14x3/2e* 6. y" - y = 1-e-2x