1. Estimate the 50% confidence limits of an auto-spectral estimate Pn for 2 degrees of freedom, that is, use X22 ; 2. Estimate 99% confidence limits of an auto-spectral estimate P for 20 degrees of freedom, that is, use X2 20%; 3. Estimate 95% confidence limits of an auto-spectral estimate Pn for 40 degrees of 2 freedom, that is, use x 40 ; 4. Estimate 95% confidence limits of an estimate Pn for 40 degrees of freedom, but 2 instead of x-40 use the Gaussian probability density function or normal distribution N(0,1) instead. [Recall the Central Limit Theorem which states that any sum of independent random variables with arbitrary probability density distributions converges towards the Gaussian Normal distribution as the number of summands (degrees of freedom) increases towards infinity.] Please explain your reasoning, interpretations, and problems encountered.