Using MATLAB
1. Assume Y is an exponential random variable with rate parameter λ=2. (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.
Assume \(Y\) is an exponential random variable with rate parameter \(\lambda = 2\). Recall that the probability density function is \(p(y) = 2e^{-2y}\), for \(y > 0\). First, we compute the CDF: \[F_Y(x) = P(Y\leq x) = \int_0^x 2e^{-2y} dy = 1 - e^{-2x}\]
Solving for the inverse CDF, we get that \[F_Y^{-1}(y) = -\frac{\ln(1-y)}{2}\]
Using our algorithm above, we first generate \(U \sim \text{Unif}(0,1)\), then set \(X = F_Y^{-1}(U) = -\frac{\ln(1-U)}{2}\). We do this in the R code below and compare the histogram of our samples with the true density of \(Y\).
# inverse transform sampling num.samples <- 1000 U <- runif(num.samples) X <- -log(1-U)/2 # plot hist(X, freq=F, xlab='X', main='Generating Exponential R.V.') curve(dexp(x, rate=2) , 0, 3, lwd=2, xlab = "", ylab = "", add = T)
Past versions of unnamed-chunk-2-1.png
Indeed, the plot indicates that our random variables are following the intended distribution
Using MATLAB 1. Assume Y is an exponential random variable with rate parameter λ=2. (1) Generate 1000 samples from this exponential distribution using inverse transform method (2) Compare the histogra...
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
Using MATLAB, not R codes, I repeat, please, not in R, just MATLAB codes, write the complete code for: 1. Assume Y is an exponential random variable with rate parameter λ=2. (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.
can you guys help me to solve this problem in mathlab Y is an exponential random variable with rate param 1. Assume eter 2. (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. Y is an exponential random variable with rate param 1. Assume eter 2. (1) Generate 1000 samples from this exponential distribution using inverse transform method (2) Compare the histogram of your...
Suppose X has an exponential distribution with parameter λ = 1 and Y |X = x has a Poisson distribution with parameter x. Generate at least 1000 random samples from the marginal distribution of Y and make a probability histogram.
#3.7 distribution. 0 and check that the mode of the generated samples is close to the (check the histogram). theoretical mode mass function 3.5 A discrete random variable X has probability 3 4 AtB.8 HUS 2 X p(x) 0.1 0.2 0.2 0.2 0.3 a random sample of size Use the inverse transform method to generate 1000 from the distribution of X. Construct a relative frequency table and compare the empirical with the theoretical probabilities. Repeat using the R sample function....
Generate 100 Poisson (λ = 2) random numbers using the Inverse transformation method, and then compare with the theoretical mean and variance. please let me know the explanaiton with detail, and r code, If not, at least python
Let X be an exponential random variable with parameter 1 = 2, and let Y be the random variable defined by Y = 8ex. Compute the distribution function, probability density function, expectation, and variance of Y
Using the inverse transform method... 4.2 Inverse-Transform Method 2, where l < t < 5, Explain how to generate values from a continuous distribution with density function/() = given u E O,1).
Using R, Exercise 4 (CLT Simulation) For this exercise we will simulate from the exponential distribution. If a random variable X has an exponential distribution with rate parameter A, the pdf of X can be written for z 2 0 Also recall, (a) This exercise relies heavily on generating random observations. To make this reproducible we will set a seed for the randomization. Alter the following code to make birthday store your birthday in the format yyyymmdd. For example, William...
Problem The random variable X is exponential with parameter 1. Given the value r of X, the random variable Y is exponential with parameter equal to r (and mean 1/r) Note: Some useful integrals, for λ > 0: ar (a) Find the joint PDF of X and Y (b) Find the marginal PDF of Y (c) Find the conditional PDF of X, given that Y 2. (d) Find the conditional expectation of X, given that Y 2 (e) Find the...