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- The density of a random variable X is f(x) = C/x^2 when x ≥ 10 and 0 otherwise. Find P(X > 20).A continuous variable Y has a probability density function for which the moment generating function is given by M(t)=e^(2*t+72*t^2). What is the variance of the variable, Var[Y]?let x be a random variable with moment generating function Mx(t)=(0.6 + 0.4e^t)^20 then the variance of x is
- Let Xbe a continuous random variable with density f (x) = 24x-4 for x > 2. Then Var (X) is equal to2) Let X be a continuous random variable with PDF 0Let f(x) is density function of continuous random variable x then the (expected value E(x Ek) = [ xfx)dx Ew) = [_fx)dx - 00 Ek) = ] -xfx)dx Ex)= | xf(x)dxA continuous random variable X is defined by f ( x ) = (3+x)^2/16 ; -3<x<-1 f(x) = = ( 6 - 2x^2)/16 ; -1<x<1 f(x) = ( 3 - x^2)/16 ; -1<x<3 a. Verify that f(x) is density b. find the meanFind the expected value of the continuous random variable g(x)= x^2+3x+2, if the density function for random variable x are shown in the following equation. f() = [F(2x-1) 0Let X and Y be two independent continuous random variables with the following probability density functions: f(x) = (1/2)e^(-x/2) for x > 0 g(y) = (1/3)e^(-y/3) for y > 0 What is the probability density function of Z = X + Y?Suppose that the continuous random variable X has CDF Fx(X) = {(x-2)/x , x>2 and 0, x=<2} a. Determine, and sketch, the pdf (probability density function) of X. b. Find the mean and variance of X c. Determine the pdf of the random variable Y=X^2The probability density function of the random variable X whose moment generating function (-) (1 + e') isLet x1,X2,.... ,Xn be a random number from a sample from the density a) f(x, 0) = 0(1+æ)-(1+0), x > 0 Find the MLE of 0 and use Cramer-Rao lower bound to find large sample variance of the estimator. Suppose a random sample of size n is taken from a population X that has pdf f(x, 0) = 0" (1– 0) x = 0,1,2,...... Illustrate that MVB unbiased estimators are necessarily MLES by obtaining MVBUE estimator of 1-0SEE 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