Question 1: How to generate an exponential IV: with parameter 1 from U(0,1)? Show all your calculations. Write a short piece of C code to generate 1000 exponential from your equation, using A=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 itu with 2=75? (if not, check your code, since this would really impact the remainder of your experiment) Please write a program to generate an exponential variable with average rate parameter 1=75 and calculate the mean and variance of the 1000 random variables you generated. (hint: function rand returns a pseudo-random number in the range of 0 to RAND_MAX uniformly; RAND_MAX: is a constant whose default value may vary between implementations, but it is granted to be at least 32,767. Important note: rand () returns a random positive integer in the range from 0 to 32,767. This function can be thought of as rolling a die with 32,767 faces. The numbers are generated by a mathematical algorithm which when given a starting number (called the "seed"), always generates the same sequence of numbers. Since the same sequence is generated each time the seed remains the same, the rand function generates a pseudo-random sequence. To prevent the same sequence from being generated each time, use srand(unsigned)time(0)) before using rand O to change the seed value.)