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Question 1:

Generate 1000 random samples of size 40 from the normal distribution with mean μ = 3 and standard deviation σ = 2.

(a) For the first sample of size 40, compute the sample mean and the sample standard deviation.

(b) For each sample, compute the value of the sample mean, so that you have a sample of 1000 sample means. Compute the mean and the standard deviation and draw the histogram of the 1000 sample means (you don’t have to report 1000 sample means, st.dev etc)

Question 2:

Now consider a binomial distribution with n = 10 and probability of success p = 0.15. Generate 1000 random samples of size 15 from Bin(10, .15). Use bernoulli random variable with probability of 0.15 to generate 1000 random number from binomial distribution. You don’t have to report the raw data.

(a) For the first sample of size 15, compute the sample mean and the sample standard deviation and draw the histogram.

(b) For each sample, compute the value of the sample mean, so that you have a sample of 1000 sample means. Compute the mean and the standard deviation and draw the histogram of the sample means (you don’t have to report 1000 sample means, st.dev etc).

Question 3:

Now consider a binomial distribution with n = 10 and probability of success p = 0.15. Generate 1000 random samples of size 120 from Bin(10, .15). Again, use bernoulli random variable with probability of 0.15 to generate 1000 random number from binomial distribution.

(a) For the first sample of size 120, compute the sample mean and the sample standard deviation and draw the histogram.

(b) For each sample, compute the value of the sample mean, so that you have a sample of 1000 sample means (you don’t have to report 1000 sample means, st.dev etc). Compute the mean and the standard deviation and draw the histogram of the sample means.