Estimate 6 by the method of moments estimator.
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- Find the expected value and variance of the random variableX whose density function is f(x) = 1/(2(x)^0.5), 1 ≤ x ≤ 4.2) Let X be a continuous random variable with PDF 0Let X be a continuous random variable with PDF 3 x > 1 x4 fx(x) = otherwise Find the mean and variance of x.25. Obtain the maximum likelihood estimates for a and ß in terms of the sample observations x1, x2, X taken from the exponential population with density functions : f (x, a, B) = yoe-B(*- ), a0 ", asx0 Y'o being the constant.Suppose that two continuous random variables X and Y have joint probability density function fxy = 1sxs2,0sy<3 elsewhere Find the strength of the relationship and interpret the findings.6) Allow a continuous probability distribution to be defined as f(x) = 4x³ for the range 0 sxs1. Demonstrate that the area underneath the curve is 1 (the function integrates to 1) and calculate the mean and variance of the probability distribution.Find the variance of the random variable X with a PDF given by 3x2 S* if - 1< x< 1, f(x) = 2 otherwise. Submit your answer in fractional form.What is the Marginal PDF of f(x)=2? Is the event independent?If the probability mass function of the variable X described in the table is. find variance Y=x^2 +4x If you know that the torque is of the second order of the variable X about the origin is equal to 2.85Given an n dimensional random sample X from a population with density f(x, 0). Show that maximizing the likelihood L(0/x) is equivalent to maximizing In L(0/x).A 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 meanQ4/ consider a random variable X with density function r6) = (4+*) { 0.5 < x < 1.5 f(x) : elsewhere Find the variance for g(X) = 3X4 + 2SEE MORE QUESTIONS