The Laplace distribution also known as a double exponential

The Laplace distribution, also known as a double exponential, has a pdf given Find the theoretical mean and variance of a Laplace distribution. Let X_1 and X_2 be independent exponential random variables, each with parameter lambda. The distribution of Y = X_1 -X_2 is a Laplace distribution with a mean of and a standard deviation of square root 2/lambda. Set the seed equal to 3, and generate 25,000 X_1 values from an Exp(lambda = 1/2) and 25,000 X_2 values from another Exp(lambda = 1/2) distribution. Use these values to create the simulated distribution of Y = X_1 - X2 Superimpose a Laplace distribution over a density histogram of the Y values Is the mean of Y within 0.02 of the theoretical mean? Is the variance of Y within 2% of the theoretical variance?

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