Problem 3: Let X = amount of weight-loss over a one week-period. Use the following piece-wise...
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)
Definition 1. A function f(x) defined on (-L, L] is called piece-wise continuous if there are finitely many points xo =-L < x1 < x2 < < xn-L such that f is continuous on (xi, i+1) and so that the limits lim f(z) and lim f(x) both crist for each a,. To save space we write lin. f(x) = f(zi-) ェ→z, lim, f(x) = f(zit), ェ→ Sub-problem 5. Let f(x)-x on (-2,-1), f(x) = 1 on (-1,0) and f(x)--z on...
Example 46. Let X be a random variable with PDF liſa - 1), 1<a < 3; f(a) = { à(5 – a), 3 < x < 5; otherwise. Find the CDF of X. @ Bee Leng Lee 2020 (DO NOT DISTRIBUTE) Continuous Random Var Example 46 (cont'd). Find P(1.5 < X < 2.5) and P(X > 4).
Problem 3. (12 points) Let X denotes the amount of time a book on two-hour reserve is actually checked out, and suppose the CDF is 2/4 0, if xs0 1, if x 22 (1) Find P(0.5 s X s 1). (2) Find P(x>1.5). (3) What is the mean (i.e., expected value for) checkout duration μ? (4) What is the median checkout duration (5) Obtain the PDF for X.
Problem 3:
Problem 3: (20 points) Suppose X is a uniformly distributed continuous random variable over [1,3]. a. (10 points) If Y - 4X2, find f (y), the PDF of Y. Indicate the range for which it applies. b. (10 points) What is the expected value of Y 0 し( 4 4
Problem 3: (20 points) Suppose X is a uniformly distributed continuous random variable over [1,3]. a. (10 points) If Y - 4X2, find f (y), the PDF of...
[EUM 114 1. Let f(x) be a function of period 2 (a) over the interval 0<x<2 such that f(x) = - f(x)pada selang Diberikan f(x) sebagai fungsi dengan tempoh 2t yang mana 0<x<2m Sketch a graph of f (x) in the interval of 0 <x< 4 (1 marks/markah) Demonstrate that the Fourier Series for f(x) in the interval 0<x< 2n is (ii) 1 2x+-sin 3x + 1 sin x + (6 marks/markah) Determine the half range cosine Fourier series expansion...
Problem 3 [5 points) (a) [2 points] Let X be an exponential random variable with parameter 1 =1. find the conditional probability P{X>3|X>1). (b) [3 points] Given unit Gaussian CDF (x). For Gaussian random variable Y - N(u,02), write down its Probability Density Function (PDF) [1 point], and express P{Y>u+30} in terms of (x) [2 points)
2x+5xy* 1) Let f(x,y) = *3+x3y2 Which among the following is true about limf(x,y)? (x,y)--(0,0) a. By using the two path test we can deduce that the limit does not exist b. By using the two path test we can deduce that the limit exists c. The limit is 2 d. None of the above O a. O b. O c. O d. 2) Let f(x,y) Vx+1-y+1 xy Then lim f(x,y) (xy)+(0,0) a. is 0 b.is c. is 1 d....
Problem 7. (6 points) Let f(x) = 5 sin(x) 3 + cos(x) Find the following: 1. f'(x)= 2. f'(5) = Note: You can earn partial credit on this problem.
PLEASE USE MATLAB
this problem you are trying to find an approximation to the periodic function /(t) esint-1) over one period, o <t < 2π. In t-linspace(0,2*pi,200)' and let b be a column vector of evaluations of f at those points. (a) Find the coefficients of the least squares fit In MATLAB, let (b) Find the coefficients of the least squares fit f(t)ndy+d2 cos(t)+ d, sin(t)+d, cos(2t)+dy sin(2t). (c) Plot the original function f(t)and the two approximations from (a) and...