Question 1: How to generate an exponential random variable with parameter 1 from U (0,1)? Show all your calculations. Write a short piece of C code to generate 1000 exponential random variable samples from your equation, using 7=75. What is the mean and variance of the 1000 random variables you generated? Do they agree with the expected value and the variance of an exponential random variable with 1=75? (Compare them with the theoretical values of mean and variance for exponential random variables). Please write down all your analytical derivations/calculations, the snapshot of your C program codes with annotations/comments, and the snapshot of your coding running results. Give explanations about why your results are correct or reasonable? Question 1: How to generate an exponential random variable with parameter 1 from U (0,1)? Show all your calculations. Write a short piece of C code to generate 1000 exponential random variable samples from your equation, using 7=75. What is the mean and variance of the 1000 random variables you generated? Do they agree with the expected value and the variance of an exponential random variable with 1=75? (Compare them with the theoretical values of mean and variance for exponential random variables). Please write down all your analytical derivations/calculations, the snapshot of your C program codes with annotations/comments, and the snapshot of your coding running results. Give explanations about why your results are correct or reasonable