[Use MATLAB]

Transformation Method using Uniform RV: Suppose that Fx(x) is the cdf of random variable we want to generate. Further let the U [0,1] be the available uniform RV. First a sample of U is selected and then a random variable ZFx(U) is computed. Now we examine the cdf of Z as follows. However, for uniform distribution P(U S a)- a and so we have P(Z x) = Fx(x). Therefore Z-FX1 (U) has the desired cdf. Algorithm: a) Generate U uniformly distributed in [0,1] b) Compute Z F(U). Part A: Generate RVs Using Transform Method 1) Write the script to generate exponential distribute d random variable X with the mean of 3 from the continuous and uniformly distributed random variable, U E [0,1]. Generate and store a large number (10,000 or more) of exponentially distributed random variable X and plot its histogram and compare with the exact exponential pdf for verification of the result. 2) Transformation Method using Uniform RV: Suppose that Fx(x) is the cdf of random variable we want to generate. Further let the U [0,1] be the available uniform RV. First a sample of U is selected and then a random variable ZFx(U) is computed. Now we examine the cdf of Z as follows. However, for uniform distribution P(U S a)- a and so we have P(Z x) = Fx(x). Therefore Z-FX1 (U) has the desired cdf. Algorithm: a) Generate U uniformly distributed in [0,1] b) Compute Z F(U). Part A: Generate RVs Using Transform Method 1) Write the script to generate exponential distribute d random variable X with the mean of 3 from the continuous and uniformly distributed random variable, U E [0,1]. Generate and store a large number (10,000 or more) of exponentially distributed random variable X and plot its histogram and compare with the exact exponential pdf for verification of the result. 2)