Question

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.

Answer 1

Assume Y is an exponential random variable with rate parameter λ-2. Recall that the probability density function is p(y) -2e2V, for y0. First, we compute the CDF: 0 Solving for the inverse CDF, we get that Fri (y) _ _ In(1-3) Using our algorithm above, we first generate U Unif 0, 1), then set

Using our algorithm above, we first generate U Unif(0, 1), then set In(1-U) X F (U) -.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 <- runif (num.samples) <- -log (1-U)/2 # plot hist(X, freq-F, x1ab-'X', main-"Generating Exponential R.У.') curve (dexp(x, rate-2) , 0, 3, lwd-2, xlab = "", ylab- "", add = T)
exponential generate graph
2 5 0 1 5 0 0 0 8 3 2 2
thank you