2 +2 111. Let m(x): 10 + 35x represent the conversion from strozzles to vinkles. Let...
1. (10 marks) random variable with density r(x). Let g: R - (a) Let X R be a (differentiable) function and let Y = g(X). Write expressions for the following ((ii)-(iv) should be in terms of the density of X (i) The integral f()d (ii) The mean E(X) (ii The probability P(X e (a, b) (iv) The mean E(g(X)) R be a smooth (1 mark (1 mark) (1 mark (1 mark) (b) Let z E R be a constant and...
(2) Let x-r cos θ, y-r sin θ represent the polar coordinates function f(r, θ) : R. R2, Compute f, (r$) and f, ( ompute * T (2) Let x-r cos θ, y-r sin θ represent the polar coordinates function f(r, θ) : R. R2, Compute f, (r$) and f, ( ompute * T
Problem 2 (5 points) Let f be a continuous function over R, and let g(x) represent a differentiable function such that 8(2)=- Given that the relationship dt = 29(x)-7 is true for all x, find the following. a) Value of g(1); (2 pts) b) Value of (2). (3 pts)
Exercise 6 (10 marks) Let X represent the positive difference between the scores obtained from two dice. a) Find the probability mass function for X. b) Show that X follows a valid probability mass function. c) Find P(X 2 2) d) Find e) Find a [Hint: An example of a positive difference is |2-6 -4. Zero is considered a positive difference.
Please complete #3. 2. Let f(x,y,z 3x2 + 4y2 +5z2- xy - xz - 2zy +2x -3y +5z. Apply 20 steps of Euler's method with a step size of h 0.1 to the system x'(t) y(t)Vf(x(t), y(t), z(t)) z'(t) (x(0), y(0), z(0)) = (-0.505-08) to approximate a point where the minimum of f occurs. Give the value of x (2) (which is the x coordinate of the approximate point where the minimum occurs). Note: This process is called the modified...
HELP WITH MATLAB PRGRAM! Please only use matlab to slove this program! Thank you! Create a 3-D mesh plot of the function Z 1 / 1 + 0.5 x + y-1 ). Let both x and y vary from-4 to +4. La e and title the plot "Jack and Jill'sHill" (be sure the single quote in the word Jill's is in the title) ex y, anď z axes T stance East n · Distance North n andĺ Height (m) Create...
4.4-2. Let X and Y have the joint pdf f(x, y) r + y, = x + y, (a) Find the marginal pdfs fx(t) and fy (v) and show that f(x,y)关fr (x)fy(y). Thus, X and Y are dependent. (b) Compute (i) μ x, (ii) μ Y. (111) 07, and (iv) 어.
2. Let X1, X2, ... , Xn represent a random sample from a distribution whose probability density function (pdf) is given by f(x: 0) = 69173-210 for r >0 and 0 > 0. Using the fact that E(X;) = 40, find the Fisher information In(0) in the random sample. (Hint: There are two different ways to compute the Fisher Information.)
Let m(t) = x2 + 3x + 5 in Q[1] and let a(t) = x+ + 4.r3 +5.22 – 67 – 9 and 6(z) = r3 +2.x2 +1. (a) (10 points) Determine whether a c) = (x) (mod m(t)). (b) (10 points) Find the principal representative for b(2) mod m().
n - meraymowa:)--00 [1] [ Let the vectors x, y and z be x = -2 y=1tz= -1 [3] [2] Find r. s and t such that y + z = x O (r, s, t) = (-2, -1, 1) O (r, s, t) = (-2, 1, 1) O (r, s, t) = (-2, 1,-1) (r, s, t) = (2, 1,-1) m Consider the set S = {w,x,y,z} of vectors in R3, S = { 121, Let V = span...