Confidence intervals

Condence intervals You are running some simulations to investigate the impact of some pa- rameter p on a performance metric X (say, the download time for some file, in seconds}. For a given value 501 of 30, you have run 400 independent simulations, to generate 490 independent samples (Xi)1:1,_,_'4m. 1. Assume that from those samples, the empirical average X' is 12.5 and the estimated variance equals 4. What is a 99% confidence interval for the expected value ElX] when the parameter is m? {Recall that a Gaussian variable with mean 0 and variance 1 is with probability c in the interval [m, ml, with {me = 2.58, (1,95 = 1.96, (1,9 = E1345.) 2. If you wanted a 99% confidence interval of size (Width) 0.1, how many samples would you need to generate (assuming the estimated variance will remain unchanged)