Instructions: If you require uniformly distributed random
numbers
in [0, 1], use Matlab’s built in uniform random number generator
rand. Also,
you may NOT use any Matlab built-in functions that explicitly
perform the task
asked for in the problem.
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Instructions: If you require uniformly distributed random numbers in [0, 1], use Matlab’s built i...
Instructions: If you require uniformly distributed random numbers in [0, 1], use Matlab’s built in uniform random number generator rand. Also, you may NOT use any Matlab built-in functions that explicitly perform the task asked for in the problem. Problem 6. Let α > 0 and set f(x)- ae-ale, for x e(-oo, oo). (a) Make a plot of f (b) Show that f is a probability density function (Hint: -, when z S 0, and x-r, when 0.) (c) If...
Let X be a continuous random variable uniformly distributed on the unit interval (0, 1), .e X has a density f(x) = { 1, 0<r<1 f (x)- 0, elsewhere μ+ơX, where-oo < μ < 00, σ > 0 (a) Find the density of Y (b) Find E(Y) and V(Y)
1. Let u be a solution of the wave equation u 0. Let the points A, B, C, D be the vertices of the paralleogram formed by the two pairs of characteristic lines r-ctC1,x- ct-2,+ ct- di,r +ct- d2 Show that u (A)+u (C)-u (B) + u (D Use this to find u satisfying For which (x, t) can you determine u (x, t) uniquely this way? 2. Suppose u satisfies the wave equation utt -curr0 in the strip 0...
Problem 6. Consider a random variable X whose cumulative distribution function (cdf) is given by 0 0.1 0.4 0.5 0.5 + q if -2 f 0 r< 2.2 if 2.2<a<3 If 3 < x < 4 We are also told that P(X > 3) = 0.1. (a) What is q? (b) Compute P(X2 -2> 2) (c) What is p(0)? What is p(1)? What is p(P(X S0)? (Here, p(.) denotes the probability mass function (pmf) for X) (d) Sketch a plot...
Let X be a random variable with probability density function 2 (r > 1 0 otherwise. (a) Compute F)-P(X ) (the cumulative distribution function) for 1. Note that F(x) 0 for 1 (b) Let u-F(z). Invert F(-) to obtain 2 marks [1 mark 3 marks) F-1 (u), (z as a function of Your function should have:- Input: n - Number of samples to be generated. . Output: x - (xi, x2,, n) A vector x of n values from the...
matlab Problem 6: The Matlab command 'randn(m,n) produces an m x n matrix of random numbers that are a realization of a white random process with some probability density function. Moreover, the Matlab command 'rand(m,n)' produces an mxn matrix of random numbers between 0 and 1 that are a realization of a white random process with some probability density function. a) Use Matlab to do the following steps: 1) Let u-randn (10000,1); and plot u. 2) Use the command 'mean(u)'...
This is a MATLAB question so please answer them with MATLAB steps. Let f(z) = V3z sin(#) and P(z) =r-x-1. 1. Find f(e) 2. Find the real solution(s) to Px) 0. Hint: use the roots command. 3. Find the global minimum for f(x). Hint: plot f over [0,2] 4. Solve f()P. Hint: plot f and P over [0,21. 5. Find lim,→0+ f(x). Hint: make a vector hi make a table [x + h; f(x + h)]". 6. Find '(In 2)....
These instructions are written with the assumption that code will be done in matlab. You might find the following built in commands useful: length, plot, xlabel, ylabel, title, legend, fzero, plot, disp, axis, axes, min, max. 2. Numerical Integration (Quadrature). Write FOUR of your own numerical integration routines. One should use left-end, right-end, or mid-points, another should use the trapezoid method, another should use Simpson’s method, and the fourth should use either Guassian Quadrature or Romberg’s method. Use your four...
1. Solve the boundary value problem ut =-3uzzzz + 5uzz, u(z, 0) = r(z) (-00 < z < oo, t > 0), using direct and inverse Fourier transforms U(w,t)-홅启u(z, t) ei r dr, u(z,t)-二U( ,t) e ur d . You need to explain where you use linearity of Fourier transform and how you transform derivatives in z and in t 2. Find the Fourier transform F() of the following function f(x) and determine whether F() is a continuous function (a)...
code in Matlab Problem 1: The MATLAB humps function defines a curve that has 2 maxima (peaks) of unequal height over the interval 0 2, f(x) = r-0.3)2 +0.01 (r-09 +0.04 Use MATLAB to generate a plot of Kx) versus x with x [0:1/256:2: Do not use MATLAB's built-in humps function to generate the values of Rx). Also, employ the minimum number of periods to perform the vector operations needed to eneate x) values for the plo Problem 1: The...