A random variable Y have a distribution with parameter a > 0 and yo > 0 if its density function is given by: ay fG) = {ya+1 (0, if y > yo elsewhere i) Derive the mean of Y. Show all necessary steps.
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- Find the minimum mean square error forecast Y(1), forecast error e, (1) and Varfe, (1)1 for the following modes. Y, = 0.8Y, +e,. Y, = 3+21+e,.The pdf of random variable X is given as ƒx(x) = Find the i) Mean ii) Mean of the square [0.3507√x 0Let the random variable X be defined on the support set (1,2) with pdf fX(x) = (4/15)x3, Find the variance of X.Let X∼Uniform(0,1) distribution. Find the PDF of Y= 3√X and derive the expected value and the variance of Y.Normal distribution. The moment generating function of a random variable U is M(t) = (1 - 8t)^-7. Find: i)Probability density function, ii)Mean, iii)Variance of U.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.Let X be a random variable with mean E[X] = 20 and variance Var(X) = 3. Define Y = 3 – 6X. Calculate the mean and variance of Y.A random variable x follows continuous uniform distribution on the interval [18,38]. Find the variance V ar (X). Answer should be with 2 decimal places.Let f(x, y) = x + y for 0 < x < 1 and 0 < y < 1 The Conditional Variance of Y when X = ; isA random variable X follows a Standard Cauchy Distribution if its pdf is given by 1 , x ER, π(1+x²) fx(x) = = 1 are identically distributed. If Y is a standard Cauchy random variable, show that Y and YLet X1, X2, ..., X50 be a random sample of size 50 from a distribution with density for 0If the random variable X follows the uniform distribution U= (0,1) What is the distribution of the random variable Y= -2lnX. Show its limits.SEE MORE QUESTIONSRecommended textbooks for youA First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSONA First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON