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- Derive that the variance of the forecasted error using Exponential Smoothing (ES) method is given by 20² Var(et) 2 – α Where o² is the variance of individual observation and a is the parameter in the ES method. =when using delta method to calculate variance, shouldn't [g'(μ)]^2 equal to (θ+1)^4?Show that the conditional variance can be written as σ^2 (X) = E { Y^2 | X} −(E[Y | X])^2 no handwritten solution.
- In a fish restaurant, population variance for fish to go bad is at least 4 days. After buying a new cooling system, its expected to be less than 4 days. After buying the new cooling system, 10 fish are tested and with an average of 8 days without going bad with a population variance of 3 days. Test with 95 confidince if the population variance is really less than 4 days. (use chi square test for the lower-side by using the formula and not the excel please)Y, = XB + ɛ, Show that the model variance in model Yi unbiased estimator ofIf X is a random variable with pdf f(x) = 2x − 2 where x = (1, 2), find the variance of Y = 2X - 3.
- The pdf is given as follows: f(x) = { (1/6)e^(1/6x) ; x > 0 0; ew] (i) Find the mean and variance of X using the pdf. (ii) Find the moment generating function of X. (iii) Find the mean and variance of X using the moment generating function.Suppose that the probability that a patient admitted in a hospital is diagnosed with a certain type of cancer is 0.03. Suppose that on a given day 10 patients are admitted and X denotes the number of patients diagnosed with this type of cancer. The mean and the variance of X are: None of these E(X)=0.5 and V(X)=0.475 E(X)=0.4 and V(X)=0.384 E(X)=0.3 and V(X)=0.291
