Develop a random-variate generator using the inverse-transform technique for a random variable X with the pdf...
Question 2 (30 pts) Suppose that X is a continuous random variable with the following probability density function: 2 /(x) = (2 _-), for 3 < x 6 0, otherwise Develop a random-variate generator for the random variable X by using the inverse-transform technique.
Given the pdf,f(x) = x2/9 on 0 < x 3, develop a generator for this distribution. Generate 1000 values of the random variate, compute the sample mean, and compare it to the true mean of the distribution
Given the pdf,f(x) = x2/9 on 0
(25 pts.) Let the random variable X have pdf f(x) = { 0<x<1 1<isa Generate a random variable from f(x) using (a) The inverse-transform method (b) The accept-reject method, using the proposal density 9(x) = 0sos
Develop a generator for a random variable whose pdf is F(x) ={ 1/3, 0<=x<=2 1/24, 2<x<=10 0, otherwise a) Write a computer routine to generate 1000 values. b) Plot a histogram of 1000 generated values. c) Perform goodness-of-fit test to determine whether these generated values fits the theoretical density function given above. Note: Invlude your computer routine for generating random variates in your answer sheet. I need numerical solution
Question Let X be a continuous random variable with the following probability density function (pdf) 0.5e fx (x) = { 0.5e-1 x < 0. <>0.. (a) Show that fx (x) is a valid pdf. (b) Find the cumulative distribution function Fx (.x). (e) Find F='(X). (d) Write an algorithm to generate a sample of size 1000 from the distribution of X using the inverse-transform method. Be as precise as possible.
a) The pdf of a random variable X is (1-μ e 26 The generating function of X is t2 -2 Use what you see to write down the Fourier transform of pdf[x] b) What is the relation between The Fourier transform of pdf[x] and the characteristic function of X? c) If the pdfs of two random variables have the same Fourier transform, then must they have the same cumulative distribution function? L.14 The pdf of a random variable X is...
5. Develop an acceptance-rejection technique for generating a geometric random variable, X, with parameter p on the range {0,1,2, ...} . (Hint: X can be thought of as the number of trials before the first success occurs in a sequence of independent Bernoulli trials.)
6. Using the mgf, find the mean and variance of the random variable X with pdf: f(x)=
The random variable X has the following pdf: 2x 0 < x < 1 fx(x) = 0 otherwise Find the s-transform of X, Mx(s) Select one: e-s 1 O a. My(s) = - + S s2 е 1 O b. My(s) = + S 52 52 O c. 1x6) = 2 (6 + 5) O d. 1 My(s) = 2 »=2(+1)
USING MATLAB PLEASE PROVIDE THE CODE. THANK YOU
1s an exponential random variable with rate parameter 2. 1. Assume (1) Generate 1000 samples from this exponential distribution using inverse transform method (2) Compare the histogram of your samples with the true density of Y
1s an exponential random variable with rate parameter 2. 1. Assume (1) Generate 1000 samples from this exponential distribution using inverse transform method (2) Compare the histogram of your samples with the true density of Y