APPLIED STATISTICS

    Project 1 Sample mean • μ is the population mean and θ=μ. If θ = X ⌢ ⌢ and X is normally distributed with mean 0 and std deviation 1 ( X~ N(0,1) ), what is the distribution of θ ⌢ look like? The number of trials is n=6. • Run a Monte Carlo simulation with 2,000 replications. • Check whether the theory is right. How? Sample standard deviation (S) • Situation: Standard normal data (~N(0,1)), for n=10 trials, • Use Monte Carlo simulation with 1,000 reps to answer these questions – What is the distribution of S in this situation? – What is the bias of S in this situation? – What is the standard error (SE) of S in this situation? – What is the SE of S when n=4 instead of 10? Central limit theorem • Generate 100 samples of exponential distribution with mean rate 2 (shown by EXPO(2)) for n=4 trials, take their averages and plot the histogram, Do X bars look Normal? • Generate 100 samples of EXPO(2) for n=20 trials, take their averages and plot the histogram, Do X bars look Normal? • Genarate 100 samples of Uniform (0, 1) for n=4 trials, take their averages and plot the histogram, Do X bars look Normal?