# How to simulate exponential random variable Y

n = 1000

# Sample X from uniform(0, 1)
X = runif(n=n, min=0, max=1)

# Choose lambda for exponential distribution
lambda = 1
Y = -1/lambda * log(1-X)

# histogram of random samples Y
hist(Y, probability = TRUE)

# theoretical density function of y for comparison
curve(dexp(x, rate=lambda), add=TRUE, col='red')