Generate an Exponential(1) random variable. (Matlab)
The Correct Answer and Explanation is:
To generate an Exponential(1) random variable in MATLAB, you can use the built-in exprnd function. The Exponential distribution with rate parameter λ=1\lambda = 1λ=1 has the probability density function (PDF) given by:f(x)=λe−λx,x≥0f(x) = \lambda e^{-\lambda x}, \quad x \geq 0f(x)=λe−λx,x≥0
For an Exponential distribution with λ=1\lambda = 1λ=1, the PDF simplifies to:f(x)=e−x,x≥0f(x) = e^{-x}, \quad x \geq 0f(x)=e−x,x≥0
In MATLAB, you can generate a random variable that follows this distribution using the exprnd function. The syntax is:
matlabCopyEditr = exprnd(1);
Here, 1 is the mean (μ\muμ) of the Exponential distribution, and r will be a random variable drawn from an Exponential distribution with parameter λ=1\lambda = 1λ=1.
Explanation:
- Exponential Distribution: The Exponential distribution is often used to model the time between events in a Poisson process (events happening independently and at a constant rate). In this case, we are generating an Exponential(1) random variable, meaning that the rate of the process is 1.
- MATLAB Code: The function
exprnd(1)is a simple way to generate random variables following an Exponential distribution with a mean of 1. Theexprndfunction accepts a parameter that specifies the mean of the distribution. For an Exponential distribution, the mean is also the inverse of the rate, μ=1/λ\mu = 1/\lambdaμ=1/λ. - Alternative Method: You could also use the inverse transform method to generate Exponential random variables manually, which involves generating a uniform random variable uuu between 0 and 1, then using the formula:
x=−ln(u)x = -\ln(u)x=−ln(u)
Here’s an example code snippet using the inverse method:
matlabCopyEditu = rand(); % Generate a uniform random variable between 0 and 1
r = -log(u); % Apply the inverse transform
Both methods will give you an Exponential(1) random variable, but the exprnd function is the more straightforward approach in MATLAB.
