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- 5)Let X1, X2, ..., Xn be a sample of n units from a population with a probability density function f (x I θ)=θxθ-1 , 0<x<1, θ>0 . According to this: Find a sufficient statistics for θ. Check if the statistics you have found are minimally sufficient.A continuous random variable has probability density function given by K(2x-3);1<x2 Find k if f(x) is a probability density function1) Let X1, X2, ..., Xn be a sample of n units from a population with a probability density function f (x I θ)=θxθ-1 , 0<x<1, θ>0 . According to this: Find the estimator of moments for the parameter θ.
- Determine E(X), E(X2) and V(X) if X be a continuous random variable with probability density function fx(x) = 3x^2 0 ≤ x ≤ 1 0 otherwiseLet continous random variable x taking on values over the set [0,a] and has a probability density function fx(x) = C exp(-nx), x = [0,a] where a = 1.1, n = 2.3. Find C7)Let X1, X2, ..., Xn be a sample of n units from a population with a probability density function f (x I θ)=θxθ-1 , 0<x<1, θ>0 . According to this: X~ f (x I θ) . Find the distribution function of the random variable X.
- Let X be a continuous random variable with range [0,1] and its probability density function is given by: f(x)=ax^2+bx+c where a , b , and c are constants. Suppose that E(X)=9/20 and V(X)=31/400 . Find a , b , and c a= b= c= Find P(0.7≤X≤1) Ans:Find the moment-generating function of the continuous random variable X whose probability density is given by f(x) = 1 for 0 < x < 1 0 elsewhere and use it to find μ’1,μ’2, and σ^2.1)Let x and y be two continuous random variables whose function is the probability density joint is given by:a)Find the conditional pdf of x given that y = Y,px|y(X|Y):b)Calculate E[x|y = Y], to 0<=Y<=1.c)Calculate Var [ x|y = Y], to 0 <= Y <= 1.