Question: 2 (a) Consider a random variable X distributed according to (1) in Question 1 with 7 4/3. What are its mean and variance? (b) Use

2 (a) Consider a random variable X distributed according to (1) in Question 1 with 7 4/3. What are its mean and variance? (b) Use part (c) from Question 1 and the rand command in Matlab to simulate 10,000 independent realisations of the random variable X from (a) and compute the sample mean. Do this 19 more times so you have a total of 20 sample means. Evaluate the mean and standard deviation of the sample means using the mean and std commands in Matlab and write them down in the box below. (c) The randn command in Matlab generates a realisation of the standard normal random variable ZN(0, 1). Use the randn command to simulate 10,000 independent realisations of a normal random variable Y with the same mean as the random variable in (a) and variance 16. Compute the empirical mean. Do this 19 more times so you have a total of 20 sample means. Evaluate the mean and standard deviation of the sample means using the mean and std commands in Matlab and write them down in the box below. (d) Repeat the procedures in parts (b) and (c) a few times so you get an idea of what's going on. Explain the difference between your observations in parts (b) and (c)

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