function is given by: ´ay§ fy) = {ya+1 (0, if y > yo elsewhere ii) Show whether or not that the variance of Y is : ayg (a-2)(a-1)²*
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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. =Let the random variable X be defined on the support set (1,2) with pdf fX(x) = (4/15)x3, Find the variance of X.If X is a random variable with pdf f(x) = 2x − 2 where x = (1, 2), find the variance of Y = 2X - 3.
- If a random variable X has the moment generating function Mx (t)= 2 - ť Determine the variance of X.Let X be a continuous random variable with PDF 3 x > 1 x4 fx(x) = otherwise Find the mean and variance of x.The input voltage to a rectifier is the continuous uniform (-1, 1) random variable U. The rectifier output is a random variable W defined by W = = g(U) = { ° U < 0 U U20 What is the variance of W?
- EX7.8) Let Y be a random variable having a uniform normal distribution such that Y U(2,5) 2 Find the variance of random variable Y.If X is a Gaussian random variable with mean zero and variance oʻ, find the pdf of Y = \X\.Show that the mean of a random sample of size n from an exponential population is a minimum variance unbi-ased estimator of the parameter θ.
- Example: Suppose that X u = (120, 80) and covariance matrix (X1, X2) has a bivariate Normal distribution with mean 6. 3 Σ= 5 What are the mean and variance of a' X, where a = (1, –1)T?Let X and Y have the joint pdf f(x,y)= x+y , 0<=x<=1, 0<=y<=1. Calculate the mean(x) mean (y) variance (x) variance(y)The random variables X,Y have variance Var(X)=36 and Var(Y)=1 and their correlation is Cor(X,Y)=−3/4. Calculate Var(X+Y) with a full explanation